The planting window for tomato seeds in Tokyo is the last week of February through the first couple weeks of March. We've been having variable weather, ranging from warm and sunny to snow. I put off planting until this past weekend to avoid the chance of frost killing the seedlings.
I bought a pack of small starting trays at the gardening supply shop and started 16 pots. Each pot has 3 seeds to maximize the possibility of sprouting. If more than one seed per pot sprouts, I'll have to perform some thinning.
To prepare the seeds, I simply ate a greenhouse tomato in January. I gathered up all the seeds that spilled out and placed them on a tissue. I folded the tissue over and rolled it up into a tube and sealed it with some scotch tape. The tissue soaks up the water from around the seeds and keeps them dry.
Before planting, I simply unrolled the tissue and cut the paper so that each seed was separate on its own piece of tissue. The seeds stick to the tissue, so I don't make any attempt to separate the seeds from the tissue. Rather, I just cut the paper into small slivers. These slivers go directly into the soil. For the past few years I've done this with different types of seeds to great success, so it might be worth a try if you are growing anything from seeds that you're collecting yourself.
Here is a picture of the starting tray with the seeds planted:
According to my notes, the seedlings will take until May to grow large enough to be transplanted. Watering will follow a weekly schedule. Keep the soil moist but not overly wet, allow for full drainage.
Next tomato update will probably be when the sprouts appear above the soil.