1) Lose your name. This might sound obvious, but it's harder than you think. If you're trying to hide, avoid using your own name. Have a couple spares that you can pull out of your pocket anytime, the more thoroughly documented the better. Obtaining a decent ID or passport is much harder than TV and movies would have you believe.
2) Don't be yourself. If you were a bowling champ or a seasoned billiards player, you will sadly have to forsake your favorite hobby. The temptation to return to old habits and locations trips up a lot of would-be fugitives. Even worse, the same goes for friends and family. You won't have to become a total recluse in your new life, but you will have to exercise extreme caution in your choice of company. Be prepared for the temptation to tell your story, or to hint that there's more to you than meets the eye.
3) Create your new origin story. The most effective ones are specific enough to sound authentic, vague enough to allow some flexibility, and dreary enough not to incite further curiosity. If you're not feeling creative, escaping an abusive/insane/toxic spouse/parent/sibling is usually a solid choice.
4) Some chemicals are your friend. Hair color is the easiest way to change your appearance, but a bad dye job might draw more attention to you. Same goes for contact lenses: keep the changes believable, and don't make any that you can't commit to full-time. (And if you have the resources and bankroll for an underground plastic surgeon, you don't need my advice.)
5) Other chemicals are not. Sadly, alcohol and recreational drugs are a classic pitfall. The inherent stress and loneliness of your situation can greatly increase your urge to indulge. And giving in to that temptation can easily lead you to compromise the cautions you'd normally take. Unless you're a world champ at holding it together when you're high (hint: you're not), keep drink and drugs to an absolute minimum. Better yet, go sober.
6) Credit cards are your enemy. In the unlikely event that you're still reading after the last item, pay in cash whenever possible. Avoid subscriptions and accounts unless you have a well-documented new identity.
7) Keep your feet on the ground. If you haven't gotten yourself a bulletproof passport, the old spinning-the-globe routine is dangerous. It's best to travel by bus or train, and to stay within borders. You'll still have a wealth of options.
8) Be camera shy. Avoiding being captured on cameras is sound advice, but these days it's nearly impossible. Unless you're wanted for something very serious, or by someone with deep pockets, the effort of avoiding cameras can be more conspicuous than it's worth.
9) Town or country. Big cities give you more people to blend in with, but also more eyes to potentially recognize you, including travelers from all over, including where you're from. If you choose a city, it's especially important to convincingly change your appearance. In a rural area, you'll draw fewer eyes but more curiosity. Being too unknown can become its own form of notoriety. A well-chosen ally who thinks he knows you can help keep gossip to a low murmur. The only steadfast rule: When in doubt, move on.
10) Change your mindset. You won't last long if you view your new life as one of deprivation. Go out of your way to appreciate what you can still do and what you still have. Come to think of it, that's not bad advice even if you decide to stay where you are.