When the tomato plant is finished, do I pull it from the ground, roots and all? I am growing my tomato in a large planter (6 by 3 feet) and hope to use the same planter next year. Also, what do you recommend to adjust the soil for the new plants next year?

I recommend pull the whole plant roots and all.

I agree with Sally. I use Mr. Mushroom compost to amend my soil. Not endorsing this product just what works best for me.

Replanting next year's crop in the same soil in your planter is an option. In the garden or farmers field, we practice crop rotation for soil health, soil fertility and disease prevention. Each specific plant pulls specific macronutrients and micronutrients from the soil that would need to be replaced because you are not rotating your crop, or composting.

I rejuvenate 'old' potting soil in containers by 'occasionally' adding an organic fertilizer, but more often using a time-release fertilizer such as osmocote, and a mineral supplement (I use azomite) mixed throughly in soil at planting time. I ESPECIALLY mix it in at the root zone level, not just dump it on top.
You can look up minerals by searching the terms: rock dust, greensand, azomite, etc.

Some ideas about both macro- and micro-nutrients? Both under-feeding AND overfeeding is a problem in planters.
https://www.harrisseeds.com/bl...

https://www.harrisseeds.com/bl...

I've had bad luck trying to add manure to my planters- I seem to burn them. Mixing in 'non-manure' garden compost is good, and I use it when I have it at planting time.

And remember to feed your plants based on THEIR SPECIFIC NEEDS. For tomatoes, to much fertilizer, especially nitrogen, will bring lots of top growth but little fruit.

Does any of that rambling help?

remove the whole plant with roots and use the soil for other plants. I usually throw the plant leaves and stems to decompose in the soil, however roots must be separated first.

If the plants showed any sign of disease or insects, it's much better to dispose of them rather than compost in place.

I never add them to compost - too much of a chance of spreading problem.