Choose a character that you genuinely care about, and can relate to to a certain degree. It makes being in character so much easier. And don't just try to look like them, try to ACT like them. Study them and watch how they move, and try to mimic it. Carry yourself like that person would. When I cosplay Cyclops of the X-Men, I carry myself seriously and a bit stiff. When I cosplay Doctor Who, though, I'm looser, more energetic and a bit more spastic.
For myself, whenever I try to make a costume, I try to find parts that are easily altered (like, for a costume of Ashe from League of Legends, I worked with a base of a little black cocktail dress ). Start off with something that doesn't demand too much detail (like armor... if you really have the money and time to invest into it, fine, but for a first time, try to avoid it as it can be quite a daunting task).
Sketch and plan early, to see what you need to buy and what you can make from supplies you already have on hand. And, above all else, don't be afraid to mess up and have fun with it