Tomato plants come in two main types- bush and indeterminate.
Bush tomatoes, unsurprisingly, grow into bushy shapes.
Indeterminate tomatoes have a really unhelpful name. They want to grow tall and less bushy, so are generally grown up supporting canes or strings into straight single stems called cordons.
Both types of tomato will grow side shoots from a main stem. With indeterminate plants you're supposed to remove all the side shoots (and later, lots of the leaves too) to help grow a plant that will produce lots of ripe fruits rather than millions of unripe small fruits. With bush plants, you're supposed to leave the side shoots on- but if you want more plants you can always take a few...
To get new tomato plants that will grow really fast and fruit almost at the same time as your seed-grown tomato plants, simply cut or pinch off side shoots and plant them. Keep them very well watered until they start to grow quickly- that's the sign that they have rooted. Then treat them like your other tomato plants, or give them away if you've ended up with too many!
Find a side shoot
Pinch off the side shoot
Make a hole in compost or soil and put the shoot into it. Press the soil gently around and water well until the new plant is growing fast
If you're growing tomatoes indoors or in a greenhouse to get a good crop, you could try planting the side shoots outside if you have space. They're unlikely to ripen as many red tomatoes as greenhouse-grown plants, but you'll probably end up with lots of green tomatoes. Green unripe tomatoes are a fantastic ingredient for chutneys, salsas, curries and for shallow frying (with or without batter)- so they're really worth having. Plus, if you bring green tomatoes inside and leave them in a bowl, they'll often ripen. Putting ripe bananas near green tomatoes will ripen them quickly as the ethylene gas bananas (and other ripe fruits- but bananas are particularly good at it) give off makes other fruits ripen.