1) START SLOW! Running is hard and if you don't ease into it, it can lead to injuries or mental burn-out as quick as you started. You might feel like this when you start, but DON'T QUIT and I promise if you stick with it you will be able to run farther and easier.
C25K plan or Another Mother Runner's 5K: Finish It plan for those of you just starting out.
2) MAKE A GOAL! In my experience, it is so much easier to run if I have a reason to run. My favorite motivation is signing up for a race to get me through those inevitable not-so-fun runs since I know I've paid for it. Other motivations could be treating yourself to new running gear or a massage after you finish a predetermined number of miles or runs.
3) GET GOOD QUALITY RUNNING SHOES! Yes, they are expensive, but yes they are necessary. The wrong shoes can lead to injury...Wal-mart does not carry running shoes no matter what the sign above them says. Go to a running store or at least a sporting goods store. Be prepared to spend some money, but unless you are excessively hard on shoes or running a lot of miles, they will last you awhile. Most shoes last 300-500 miles. Find shoes that are comfortable for your feet. Fit is the most important thing. You might not be able to wear the same shoes as your friend, sister, co-worker etc. and if they aren't comfortable, don't buy them. Walk or even run in them around the store. Some stores will allow you to run on the sidewalk in front. And make sure you know the return/exchange policy in case they still don't work out for you.
4) DON'T COMPARE YOURSELF TO ANYONE ELSE! The great thing about running is that it is individual. You can have your own victories even if you never win a race. It is super easy to fall into the trap of looking at the miles or the pace someone else runs (especially if you read blogs!) and start being hard on yourself. Run what you can at the pace you can and enjoy it. The other thing I have to work on is not comparing myself to my former high school/college running me. I am not at the same point anymore and it's ok, but the joy of running gets sucked out if we are always looking at someone else or previous achievements as the standard.
What's your #1 tip for new runners or runners starting up again?