What's most important is to consider what state the tomatoes are in.
If your tomatoes are not fully ripe, allow them to ripen at room temperature first.
Once fully ripe, either use them within a few days or extend their shelf life by refrigerating them. However, refrigeration can alter their texture and flavor, so it's best to bring them back to room temperature before consuming.
Note that refrigeration stops the ripening process (in case you picked too many ready-to-eat tomatoes and want to extend their life by a few days.
With an abundance of tomatoes, you can preserve them by canning, freezing, or drying. Instructions and recipes will be posted next week.