This might help in understanding the new growth to prune out.
http://www.taunton.com/finegardening/how-to/ar ticles/pruning-tomatoes.aspx ...
There are differing opinions (as in all matters gardening) about the efficacy of pruning. The benefits definitley include better air circulation for the plant to help in controlling fungal attacks, as well as earlier and larger fruits. On the down side is the fact that the number of fruits will be diminished.
Don't over-fertilize. just an occasional (every two weeks) light application of a balanced fertiliser will work. Fertilizers will have a series of 3 numbers to designate the percentages of nitrogen, phosphorous and potassium. Generally speaking, the numbers should be about equal to one another, say 10-10-10 or so. tomatoes like moist but well drained soil, so mulching the soil around the base of the stem with peat moss keeps them happy. Best of luck!