Hey guys, recently I've been learning a lot of This Town Needs Guns songs. For me, fretting the notes isn't the problem for me it's the finger picking. Are there any good exercises that I can practice to help improve my overall finger picking technique?
Basically it's going to be the same principle as playing with a pick; it's not the exercises that really make the difference, it's making sure your movements are small and relaxed.
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Also remember that you need to work on the synchronization of your left and right hands, else no matter how fast you get that finger picking you won't be able to play much with it.

Basically you could just practice that song instead of exercises; Slow it down to a speed you can play it, make sure your movements are small and relaxed (as Zaphod said) and make sure you're playing every note clean (you can play exercises as well if you want).
If you're looking for specific exercises to help with fingerpicking, you can never go wrong with mauro giuliani's 120 right hand studies (pdf's of it can easily be found online). Even though they're geared to classical guitar, I still practice them on both my classical and steel string.

Although practicing them without proper technique won't be very beneficial. Ensuring what Zaphod said, it's just practice beyond that.