Tip #1: Fill the frame with your subject
The cosplayer put a lot of time and effort into making the outfit, the least you can do is to fill your picture with the time and effort they have put into making the outfit.
Tip #2: Subject Isolation
|This gwendolyn cosplayer was shot with a 24-70L at f2.8|
It is very hard to do this with a regular point and shoot because of the small sensor size. On an APS-C or a Full-Frame SLR it is much easier to create subject isolation. The rule of thumb for SLR's is that there is more subject isolation with larger apertures.
With larger apertures you can create a blurred background (known as bokeh). In my personal experience a zoom lens with a constant f2.8 creates very pleasing bokeh. A prime lens such as a 35mm f1.4 or a 50mm f1.2 creates great bokeh. The downside of such primes is that under f2.0 the depth of field is so small that the chance of error increases exponentially.
Tip #3: Rule of Thirds
This is a rule that is easy to break once you get a handle of good composition, but when done right it always impresses.
Photography during an Anime Convention is hectic, which means that each shot is important. As long as you follow these basic tips your cosplay pictures will always be fun and interesting to look at.