Forearm Workout

What are the best ways to build up your forearm in a standard home gym consisting of a bench, barbells and dumbells.

I would have a good look through people journals who use a home gym and base your routine on the people who have similar goals to you.
Then post a routine up and we can critique it
rather than just ask for best exercises as a routine is more important than singular exercises.
Plus once the reply start coming in. The people will differ on there preffered exercise as well.

holding heavy things :)

For someone of your level I wouldn't do anything specifically for your forearms. As The West says, holding heavy things, although sounding rather primitive, is the way to strengthen the forearms. Rowing whilst holding said heavy thing will also have the benefit of building the back and arm muscles too.

If you approach training by looking for exercises for every single muscle in your body, you're going to end up with a routine consisting on 87 exercises that is a big fat waste of time.

Have a look at some of the routines in the BBing Routines forum and try and base your training around big compund exercises (Squat, Deadlift, Bench, Dip, Row, Chin/Pull Up, Overhead Press).

Far better in the long run than a multitude of exercises for each bodypart.

I find deadlifts, rows, pullups and barbel curls work forearms enough so I have no need to do specific excercises for forearms.