Most of these tips & tricks are things that I came across and found handy, but I don't know who originally came up with them. Maybe there are some tips for you as well :)
Alcohol: Can be used for transferring newspaper text on to your nails. Cut a piece of paper, place it on your nail and hold a cotton pad with alcohol on it for a few seconds. You can of course go for a simple piece of text, but using QR codes or an Asian newspaper with symbols gives a nice result too!
Broken or chipped nails: You can fix these with silk wraps and nail glue (unless the part that's broken really broke off completely of course). Clean the nail, place a piece of silk wrap on it, cover it with glue and let it dry. It's handiest to have glue with a brush, but others work fine too. If needed you can place another silk wrap with glue on top of the first. File it until it's smooth enough with a buffer file, use a ridgefiller if wanted, and done! You can remove the wrap again by gently filing it off or with remover that contains acetone. It won't come off straight away though, so you can use acetone remover for your normal mani as well without having your wrap come off. If you don't have silk wraps, try one of those pyramid teabags, I used those before as well and they work fine too!
Cling film (also known as Saran wrap): You can use cling film for a funky effect on your nails. Apply a basecolor and make sure it's fully dry, then apply a second color and while that's still wet, dab it with a little ball of cling film. It'll take off some of the polish, so your basecolor comes through again. Top coat and done! If you dabbed off too much, just use a little drop of polish on your nails and continue with the foil.
Closed bottles: If a bottle won't open anymore, you can try several things to open it. Warm water can work, a big rubber band wrapped around the cap can help because you'll have more grip that way, or using pliers or the inside of kitchen scissors (the round metal part with teeth). The pliers or scissors will leave marks on the cap, but it does work. Don't forget to clean the top of the bottle and inside of the cap once it's open, so it won't happen again :) And here's a tip from one of my readers (thanks Amanda!), you can also use a hairdryer to melt the polish that's holding the cap shut and it'll come right off.
Corrector/remover pens: A lot of people use brushes for cleanup, but I haven't found a brush that I like yet so I use these pens instead. If you dip them in remover and wipe them off in between, they last you for quite some time as well. If they get a bit fuzzy you can still use them, I usually have 2 that I use, one that's still sharp and one that went a bit fuzzy. The fuzzy one I use for the rough cleanup after stamping.
Cuticles: I never cut my cuticles or anything like that, using a cuticle remover every now and then works much better if you ask me! I'm using the Nfu.Oh Cuticle Remover or the Essence Fast Cuticle Remover and I think they both work great. I put a bit on all cuticles of 1 hand from thumb to pinkie, then gently go past my cuticles in the same order with a rosewood stick, clean it and do the next hand.
If you have a hard time not picking on your cuticles (or well, in this case more on the sides of your nails), making them very rough, you can try to gently file it a bit smoother with a file that isn't too gritty, like the first step of a buffer file. I used to bite nails and the sides as well, keeping it more smooth like this made it way easier to stay off it!
Feathers: You can use real feathers on your nails, cut them a bit in the shape of your nail, glue them on and when it's dry you can carefully cut them further in shape. Finish the mani with top coat.
Filing: Never clip your nails but use a glass nail file instead. Your nails are made out of layers (which you can clearly see when they chip) and clipping them puts pressure on these layers. Always file in 1 direction, and use a less gritty file or a buffer file to smoothen the edges when you're done. It takes some time, but as with most things, the more you do it the faster and easier it goes.
Since I'm using a glass file my nails really improved, less chipping and stuff. A good glass file costs a bit (mine was €10), but will last your for ages, and you can just rinse it off after using it. A cheap one will lose it's grittiness quite fast.
If you find it hard to get a nice shape, file your nails while they're still polished. The white part of your nails isn't always straight, without seeing that part it's easier to file straight.
Glitters: Doing a cleanup after applying glitter polish can be annoying, for me it helps to use a basecolor first and do a cleanup, then apply the glitter polish. With the cleaned base below it, it feels easier to stay within the lines with the glitter polish.
Applying chunky glitters is almost impossible when you just polish them, it's easier to dab them on by pressing the whole brush flat on to your nail, and dab your whole nail like that.
Gloves: If you use cleaning gloves, you can wear cotton gloves under them to prevent your hands from getting all moist, and if you want, use a handcream under those. Soft hands after cleaning!
Half empty bottle: When a bottle is almost empty and it gets annoying to get it out, I just start with a new bottle. Once there's enough out of the new bottle, I put the old bottle upside down on top of it and let it drip completely empty. I haven't had to do this with polish yet, but with base/top coat I always do this.
Images plates: I store my image plates in a businesscard folder, this way I can always browse through the plates easily :) *Update* I now use a plastic folder with sheets for cards (Magic cards, sports cards, ...) and it works fine too! And some brands now offer a platefolder as well.
Latex gloves: These come in handy when you want to clean up stuff with remover and are afraid you'll ruin your mani. I usually clean the materials I used when I take my mani off again though, but they're also handy when you want to change your pedi but not your mani. Your hands might get a bit powdery, but that's it :)
Lip balm: If you don't have any cuticle creme nearby, a lip balm can do the trick too. I'm not sure if they all work as well, but I have one with only natural ingredients and that one works nice.
Loose pigments: You can use these for frankening (mixing polishes and/or pigments to create a custom polish), but you can also dab some on your top coat when it's still wet. Then add some more top coat to seal it in.
Nail wheel: I always buy the clear ones, so it shows much better if a polish is sheer and how many coats it needs. You can polish the wheels by brand, by color, or just random. I'm polishing them random, just filling them up when I get new polishes. I also made seperate wheels with all my stamping polishes, so I can easy hold them next to other polishes and find a nice match. *Update* here's how I organize my stash nowadays.
Needle: You can create a tie-dye or marble effect with the help of a needle, toothpick, or something else thin and pointy. Apply the colors of your choice, and while the polishes are wet, gently drag the needle from one color to the next and back again.
Placemat: I use a plastic placemat as surface for all my polishing, and I find it ideal! I use it to practice things on, polish on to see if colors match or test out some layering, test mix polish for frankens, you name it. When I'm done, I just wipe it off with remover and it's ready to go again. You can buy placemats with the weirdest designs, but I'd suggest to take a neutral one so you'll always see the polish in the right color.
Rhinestones: You can apply rhinestones with nail glue, but for me top coat works fine for most rhinestones and is less nasty to work with. I put a drop of top coat on my placemat, dip in it with a pointy stick (like a toothpick or the pointy side of a rosewood stick) and touch my nail with it where I want the stone. Then I use the same stick, pick up the rhinestone at the colored side and place it on the top coat on my nail. I find it easy to pick the stones up like this, because there's still a bit top coat left on the stick after putting some on my nail. The nail has more top coat than the stick and the stone will usually attach to the nail straight away. Seal them in with a layer of top coat and done.
If I use rhinestones in a funky shape (like star or flower) I don't use top coat on them, but use them on top of the top coat with nail glue. I find that top coat can make it a lot less clear what shape it is, and this way it doesn't last as long but you can see the shape better.
Sandwich: Holographic and matte polishes often chip faster, but using a top coat dulls the holo effect a bit or removes the matte effect of course. To solve this you can sandwich the polish, which means you use a layer of top coat between the polish layers, and end with polish instead of top coat.
Shrinkage: If you have shrinkage of your polish, which can be caused by some top coats as well, try to wrap your tips next time. Works like a charm for me!
Smudged polish: Just applied polish and smudged a nail? Lick your finger (yeah I'm not kidding) and use your wet finger on the smudge, carefully making it smooth again.
Stickers: If you have a hard time picking them up from the sheet, try using a hobby knife.
Straws: You can make a splattered manicure by dipping straws in polish and blowing the polish through the straw on to your nails.
Thick polish: If your polish or top coat got all thick and goopy, use a polish thinner to restore it. Never use polish remover, the remover will break down your polish, while with polish thinner a bottle can last you for years. Here you can see the result of old polish with thinner.
Top coat: If you want to do something different with your top coat, try stamping on a matte mani with it!
Vaseline: If you're going to watermarble, you can also use vaseline instead of tape to keep your fingers clean. Products like cuticle oil work as well.
Watermarble: If your polish isn't spreading well you can try using filtered or bottled water, but I noticed that some of my polish just doesn't work so good for marbling. Keeping the brush near the water instead of higher above it seems to help as well. For a dry watermarble, have a look at the ziplock bags How To.