Indoors. And you need to tend to them gently. They come along though. I usually buy a Container of Mini Cupcakes and Cherry Tomatoes in March and put potting soil and some seeds in there. They sprout.
Need to be started indoors. When big enough to be transplanted, take a week or two to harden them off. Here are some sites to get you started.
You can begin seeds indoors or wait till after the last frost and direct seed into the ground.
You may find these articles helpful for starting seeds indoors.
Paper pots are also good for starting seeds:
Another option and my favorite is the seed starter box because you can keep the mess out of the house.
If you are growing them for the better flavor of heirloom seeds then it is worth it but it is a little costly to get started. Just FYI, the heirloom seeds are not resistant to the funguses and wilts as the newer varieties so you should probably start a weekly spraying of something like Safer 3in1 garden spray soon after planting outdoors.
Here are some things I wish I had known in advance:
Start them 6 to 8 weeks before the temp is expected to stay above 50. Usually the last frost date is way to early. You need, seed starting medium, potting soil, grow lights and an adjustable way to suspend the lights an inch above the plants as they grow. You probably need about two feet of head room. A timer and a heating pad(s) are recommended. You will need progressively larger pots to transplant them into as they out grow the starter flats. So that will take up more space and maybe more grow lights and heating pads. And plan on some kind of tray for the larger pot to sit in. Don't grow too many pants unless you don't mind throwing away the extras. Happy gardening. Here's wishing you beautiful and delicious tomatoes.
All I do is take a slice of tomato and place it in a pot , cover it with dirt and you can grow tomato anytime, inside or out.