I grow tomatoes in cntainers every year including cherry tomatoes. Here's what I do:
Choose tomato varieties which are good in containers, such as Veranda Red, or Sungold. If you're not sure, it will say on the seed packet what the best growing conditions are for them. I also like doing hanging basket cherry toms, so I get a lot of Tumbling Toms as well.
Start with a seed planting tray and some seed compost, and plant a few seeds, maybe twice as many as you think you will need plants for. Pop them in a warm spot, inside on a windowsill is good. Keep them damp but not soaking. They should germinate in about 1-2 weeks in my experience.
Once they start to grow, you will see which are the strongest ones. When they get to about 3 inches tall, you can plant them on into your final container, and place them in their outdoor spot. I usually use an all purpose compost for these containers, with a bit of tomato food thrown in.
Note, if you want to skip all of this you can order small plants, usually called plug plants, direct from seed suppliers like Suttons or DT Brown, they will post them to you.
Depending on the size of your container you may be able to do more than one plant per container, but one plant will want about a foot of space around it once it's full size, depending on the variety.
After that, just keep watering it, give it the odd bit of tomato food, and chat to it occasionally (well I do, anyway) and you should wind up with lots of lovely cherry tomatoes.