In college my friend and I actually made and sold t-shirts to pay off parking tickets :)
We found the best way was to stand in the middle of the most popular area for student traffic and loudly advertise what we were doing. This method worked extremely well for us and could work for others.
However, for your idea it might make more sense to advertise online using site like Google for their AdWords search platform. This will allow you to advertise your website to anyone who types in searches like "t-shirt" or "custom t-shirts" or whatever searches you want to target your ad to.
Another way is to go on LinkedIn and find out who the Human resources decision makers are in different companies you are looking to sell to. You can directly reach out to these folks and start conversation regarding your product.