The more experienced players here may have additional advice directly relating to finger independence, but I found this just happened with time, practice and appropriate exercises.
You'll find some stretching (IMHO a good place to start) exercises here, including Kirk's Ultimate Fingerstretching excercise:
Finger stretches
Kirk's lesson may be a bit advanced at this stage, but something to work towards. Watch it, anyway just for fun. Whilst you're in YouTube have a look at this beginner level video by Justin Sandercoe:
YouTube - 097 Guitar Lesson - Finger Stretching Exercise
Hope that helps.
Cheers.