As a beginner...you're supposed to have this problem. It bugs me when I see people who should know better do this!
All of your fretting hand fingers should be on the strings...ready for action. You may need to pivot your fretting hand a little more towards your body with fingers curled(like Matt said, "A C-Shape")
Guitarists generally play with more of a 'angled' approch with their fretting hand(good for chording?).
It's been posted here before...
A decent exercise is to put your fingers-per-fret on the G-string:
Index finger at the 9th fret
Middle finger at the 10th fret
Ring finger at the 11th fret
Pinky at the 12th fret
Move ONLY the index finger...barely off the string, up & down. If the other fingers don't stay put, use your plucking hand to keep them still.
Then put the index back on the string & move ONLY the middle finger. Etc.
Eventually, toggle between the index &, say, ring fingers. Again, move only those two fingers up & down/back & forth while keeping the middle & pinky fingers stationary!
Then, move only the index to the D-sting/9th fret...followed by the middle to the D-string/10th fret, etc.
(this is similar to Steve Bailey's "Hazard Exercise")
Note: This may be boring but it is something that is oft-neglected. If you can do the above to a metronome...you can kill two birds with one stone.