What's the best way to eat really fresh tofu? My favorite every time is hiyayakko (cold tofu), but agedashi-dofu (deep fried tofu with dashi sauce) is a close second.
Hiyayakko is plain chilled tofu with a little garnish on top. You can add any number of garnishes, but my favorite is simply finely chopped green onion, grated fresh ginger, and bonito flakes, with a little sprinkle of soy sauce. Don't add too much soy sauce or it will mask the delicate flavor of the tofu. In the summer months I could eat this every day. At least half of my square of home made tofu gets eaten as hiyayakko every time. In the summer, some finely julienned shiso leaves make a nice addition too, as are toasted sesame seeds, red chili powder, and so on. Think of what you might like to put on top and go for it!
Agedashi-dofu is deep fried tofu with a simple dashi-stock based sauce. It's not the same as aburaage (thin deep-fried tofu) or atsuage (thick deep-fried tofu), since agedashi is coated with flour and meant to be eaten right away. It's a very delicate dish, so be sure you are ready to serve this immediately.
The key to deep frying tofu is to press it a bit so that excess water is drained out of it. To do this, wrap the tofu piece in a cloth or in a couple of layers of paper towel, place on a cutting board, and place another cutting board on top. Put a cup of water or some other small weight on top of of the covering cutting board and leave to drain for about 30 minutes.
In the meantime, make a simple sauce of 4 parts dashi stock  to 1 part plain soy sauce, and keep warm. If you have a bottle of mentsuyu (concentrated noodle soup base) or you've made my Japanese essence , you can use this also, diluted with hot water at a 5:1 or so ratio. Grate some daikon radish to put on top.
Unwrap and wipe the tofu, and coat in white flour, Fry in fresh peanut oil until a light golden brown on all sides. Drain well, put a couple of pieces into a small bowl, put plenty of grated daikon radish on top, and pour the dashi sauce over. Eat while piping hot.