If you are good enough to do it on the "fly" then a headset mic (from shure or senheiser, they are the best) can be done either directly to an audio desk for mixing later on or directly to the film if your camera has DIN inputs.
The best way I have found to do it is to record everything visually and add sound later.
Example: Filming is done with puppets saying their lines. After this all audio is done as "voice over and fill in" after the fact. This eliminates all puppet and set sounds and lets you only add the sounds and voices that you actually want.
This is easy because you are still recording what the puppets are saying, so even for improv stuff you can voice over what the puppet has said because you are going to overdub what has been said anyway.
For many voice actors this is the way it is done. In a studio after the fact.
(your computer can make a pretty good sound studio with the right software and equipment. Using Adobe Audition and a descent mic you can make the audio very professional.)
Peace