What's the best method for printing a design on a t shirt?

If it is only 1 or 2 colors, I would make a stencil and use a roller with fabric paint. I have also made t shirts with lino block prints. If it is a more complicated design and of many colors then a computer generated transfer would probably work.

We’ve used iron-on transfers recently as @rooeytoo suggests and that’s the easiest method for sure. The downside of the transfers is long-range durability, they will inevitably crack a bit after several rounds in the laundry. They work best with designs that have large features (e.g. big words) that don’t loose as much appeal when the crackling runs through them. (“Area Man For World Peace” is still readable/wearable ten years after Iraq war protests.)

I’ve done Silk-screen, stencils, and block prints in the past and it’s clear that with good fabric inks any of those methods will all be more durable.
The size of your design and the amount of detail could direct you to the most appropriate medium.
– a lino block is easy to make and use for a small design. It works like a stamp so the target fabric has to be very flat for even printing. Also, evenly loading your block with ink is harder as the block gets bigger. You can achieve pretty fine detail with a lino block though and they last well for many prints.
– stencils work well with large features, and if you make them out of acrylic film they can be pretty durable. A stencil accommodates imperfect flatness pretty well as you’re painting through the stencil with a brush or sponge. Downside of a stencil is difficulty with small details.
– silk screen is the choice of pros for a few reasons. You can screen a lot details if you need that and have a large design and if you have your method down you can get prints done quickly.

Try just simplifying it and drawing it with fabric paint. Draw out the design first and then redraw it on the shirt.
Silk screening is more expensive now than ever. Unless you are doing multiples, the $20 you spend on the screen+ink makes it a little pricey. When people come into our shop-we tell them the costs of doing 1 shirt and also the advantages of doing the shirt themselves. I could charge them for each screen, the inks, the artwork ect. But, the cost is a little much for 1 or 2 shirts. I have seen some brilliant work on individual shirts. I’m just talking from a professional level.