The 'off of' combination is part of an informal expression sometimes used in the USA. It means the same as 'off', and as Simon suggests, it's probably best avoided. This sentence means that we are going to use what we learnt yesterday ('the material from yesterday') as a basis for further training, and we're going to expand and develop on it. I would use the phrasal verb 'build on' in this situation. You build on what you know.

It's bad English to say that. However, I have to admit I often say things such as, "Don't jump off of the roof! It's too high!" What I mean is Don't jump off the roof!" Somehow that little 'of' adds itself in! I think it's because we hear a lot of bad English... from native speakers (!) and we get into bad habits ourselves. We all have bad habits. That's one of mine!

Another way to express the same idea, which may clarify the ideas communicated, would be like this: "We're going to use yesterday's experiences and use the tactics to lperform better. However, sometimes the phrase "to build off of" is seen and heard. It would appear in this manner: "Let's build off of our defeats and march on to victory." "We can learn from our defeats, and build off of the experience of despair and failure to obtain the championship." .These are examples I suppose, from inspiring athletic subjects; but one can see how the phrase can be used in almost any activity. .

It's really bad English to use 'off of'. It's much better to say: We're going to build using the material from yesterday and now use both of the tactics to learn better.