The simplest tool for sowing seeds is a dibble stick. This is really nothing more than a small stick a gardener uses to dig a hole for seeds. You can use pencils, paperclips,screwdrivers, toothpicks, and all kinds of other items as dibble sticks. As a rule, seeds should be sown in a hole roughly 4 times their width deep. Lettuce and carrot seeds, for example, will be just barely covered while larger beans and pumpkin seeds will want to be planted a little deeper (~1 inch).
For crops with smaller seeds that are planted densely in rows, you can make a small furrow in the soil and drop a row of seeds into it. This can be done easily with a hori-hori and is a little faster when planting things like carrots and radishes. The soil is then smoothed back over the furrow, burying a row of seeds at the desired depth.
Start sowing seeds as soon as the weather is warm enough to move transplants to the garden. Plants grown directly in the garden will be a little more robust and well adapted to their environment than transplants, but will be a few weeks behind. Just like starting indoors, there is no need to make scheduling complicated. New plants are inexpensive and easy to make so just keep planting more wherever there is space.
Especially in early spring when it is cool out, seeds will take more time to sprout than you might expect. Keep in mind that crops like kale or spinach can be planted very early, but may take as long as a couple weeks to sprout if the weather is cold. Just keep planting new ones as long as you have space. Once seeds start coming up, you can go back and replant spots where seedlings didn’t make it.