Growing Basil and Thyme in Pots

I have a couple of questions concerning how to grow herbs in pots. I live in an apartment with a small patio facing west. First question is how can I grow basil that wouldn't die on me. I had a plant last year which I got from cuttings. It grew beautifully for a few months then it began to wilt and finally died. I love basil and would like to start all over again but I need some advice as how to do it right this time.

Basil is susceptible to a fungus disease called fusarium wilt which attacks the stems causing brown striations followed by sudden wilting and death. The disease is spread on seeds but it can also spread by infected tools used to harvest leaves or make cuttings.
Even if you do not have a fusarium problem, the plants may be reaching their natural mature state in which they become weaker. This happens to annuals after they flower and set seeds. You can sometimes delay this natural death by old age by picking off the flowers as they open so they do not set seeds. Setting seeds seems to signal the senescence stage in the natural life cycle of basil.
It also helps to provide as much light as you can. You should consider setting up a light stand with full-spectrum bulbs. Full-spectrum incandescent bulbs rated at 100 or 150 watts work well when placed within 12 inches of plants and if turned on for 18 hours daily. We recommend keeping the plants in a south facing window so that they get both natural and artificial light.

Second question. I have a thyme planted in similar conditions as the basil, a large plastic container set on the patio. It is surrounded by a very large geranium that for a few months covered the entire thyme completely. Now the thyme is looking spindly and dried in some parts. What can I do? I moved it away from the geranium but it doesn't seem to be doing much good. Also I have been giving it fertilizer once a month.

As long as there are live leaves the plant will eventually develop new growth. It may not be possible to get new shoots from the woody spindly stem, but with judicious pruning of the growing tips you may be able to get new shoots to develop lower down the stem. There is no need to fertilize unless the plant is showing signs of active growth. It is important to realize that fertilizer does not jump start growth; it only promotes growth in plants that are already growing. Probably the most important thing you can do is to make sure the plant is getting full sun.