Of all the things a grower can do to get a crop of tomatoes, providing supplemental nutrients is probably the most often misused and abused so this is a not an easy question to answer. A tomato’s nutrient requirements change as the plant grows. Also, the soil the plant is growing in may have excess amounts of some nutrients and too little of others. The first recommendation is to get a soil test to know its current status. A general fertilizer recommendation is that the Phosphorus content should be higher than the nitrate content and the Potassium content should be between the N and P values. For example, 8-16-12 would be a good general mix to use. Many growers do fine with 13-13-13 though it is not well balanced for tomatoes.
I strongly recommend using organic fertilizers if available. Taste and growth are both better than with commercial fertilizers. Various animal manures such as cow, horse, rabbit, etc. are all acceptable if they are free of contaminants and weed seed. Composting manures before use is highly recommended with the exception of rabbit manure which can be used fresh with excellent results. High quality compost made from yard waste or other vegetative matter is another excellent source of nutrients. Special purpose fertilizers such as blood meal may be appropriate in some conditions.
In general terms, manures make excellent fertilizers. Rabbit manure is one of the best since it can be applied fresh and won’t burn plants plus it is nearly PH neutral so helps with acid soil. There may be problems with manure from cattle feedlots since large amounts of salt are fed and accumulate in the manure. Chicken manure or chicken litter are excellent also but beware, it is high in nitrogen and can have the most obnoxious odor imaginable. Cow manure is a good supplement and I've read articles about several people cleaning out stables for horse manure and straw. The problem is that the straw often contains seed which grow in your garden. Either compost these manures to kill the weed seed or else get ready to do a lot of weeding.
The best ways to use manures for fertilizing are to apply to the soil and work it in at least a month before planting or to compost it and apply to plants when it is well decomposed. A tomato plant can use up to 10 pounds of dry compost in one growing season depending on what the compost is made from. This is roughly equivalent to 30 pounds of fresh (wet) rabbit manure. It is best to avoid sidedressing with fresh manures since there is some possibility of spreading diseases. If you do sidedress, bury the manure next to the plant rather than just applying to the ground surface.
Tomatoes need additional nutrients about one or two weeks after transplanting to their permanent home. They need fertilizing again just as first fruits start to form. A general recommendation is to use 1 level teaspoon of commercial fertilizer and at least a quart of compost for the first fertilizing, and use 1 level tablespoon of commercial fertilizer and a half gallon of compost per plant for the fertilizing at fruit set. It is very important to give the plant some supplemental nutrients at fruit set. This extends the duration of plant expansion which results in much higher overall production. Depending on the plants, indeterminates may need a third or even a fourth fertilizing to maintain productivity in long season areas. Some growers use slow release fertilizers such as osmocote. See the seedling section for information about their fertilization requirements.
Here is a link to a document that was published by NNGA Nutshell about 60 years ago. I need to dig up the attribution. You will like it! Ortho Phosphate