there are few ways of doing that, ferny - all depends how much time(patience) or money you have and how many copies you need.
1. Screen printing or silk- screen printing - the most 'proffesional' method for more copies - i have no idea if thats the correct word for it, here its called 'sitodruk' (santino? ola? can you help me with this one?-

) - what you have to do is design a logo and give it to the printing company - that's all -> 'sitodruk' is one of the best ways of printing on fabric, and its very durable , its also not VERY expensive - but - they prolly wont print you one or two copies i think, but you can always try and ask-

...ah, and this method is much cheaper when you use only one or two colours, and when the design is more like 'sign' - images, pics , paintings, very colourful things with mixed colours - all those things dont work well with 'sitodruk'.
2.Thermal - Xero method.
you can do it at all biggest 'xero companies' (or labs)-> the method is not that durable as 'sitodruk', but its much cheaper (here its about 30 zl <its few dollars i think> for a printing AND a shirt), and you can print one copy or two if you want to.
- you can give the digital file to the company, you can give them a print, design, image at the sheet of paper, whatever you want - and it lasts few minutes to put it at the shirt. Usually they have size limit which is A4.
Ive tried it once - it looked very nice, but after few times in washing machine - it has dissapeared.
3. Acrylic paints. They are indestructible.
This is the way i use the most.
There are special acrylic paints, but called 'textile'(or something like that) - not the ones u use for painting - special ones for the fabrics (textiles? )
After you finished your painting you have to harden it with an iron for 5 minutes - then the painting is indestructible. I have made some t-shirts with this method few years ago and the colours are still vibrant and nothing wrong has happened to it.
The paints are pretty cheap, and you buy every colour separately, so its even cheaper, cause sometimes you dont need the whole colours.
If you are interested with this method and tricks how to make it work better - just pm me - i have a bit of experience with it, ha ha
hope it helps. and hope it works in english, he he
good luck with it, ferny!
anj