You'll need to look at the libavcodec documentation - specifically, at avcodec_encode_video(). I found that the best available documentation is in the ffmpeg header files and the API sample source code that's provided with the ffmpeg source. Specifically, look at libavcodec/api-example.c or even ffmpeg.c.
To force an I frame, you'll need to set the pict_type member of the picture you're encoding to 1: 1 is an I frame, 2 is a P frame, and I don't remember what's the code for a B frame off the top of my head... Also, the key_frame member needs to be set to 1.
Some introductory material is available here and here, but I don't really know how good it is.
You'll need to be careful how you allocate the frame objects that the API calls require. api-example.c is your best bet as far as that goes, in my opinion. Look for the function video_encode_example() - it's concise and illustrates all the important things you need to worry about - pay special attention to the second call to avcodec_encode_video() that passes a NULL picture argument - it's required to get the last frames of video since MPEG video is encoded out of sequence and you may end up with a delay of a few frames.