Not Recommended Methods
Feel free to try any of these. I just don't personally feel they are worth it.
T-shirt transfers - This is the only method I've ever tried in making my own shirt. You buy t-shirt transfer sheets, print out a design, and then iron them on. What could be easier, right? Well, I never like the way they looked. It's very obvious that you transferred something onto the shirt. I just doesn't look good. This guy seems to have the process all figured out. But I will tell you that my shirts never looked that good, and I never figured out how to prevent the image from fading after a few washes.
Design and Buy Online - Here's a site I found where you can design your own t-shirt, buy it, and have it shipped to you. That also sounds pretty simple. But it's $19 for the shirt (and who knows how much for shipping). There's cheaper ways to go about it.
Screen Printing - This one is way too involved and costly to attempt it. But you can do it, and have a great looking shirt at the end. You can even find screen printing kits on Amazon. But I believe there are simpler methods that can achieve similar results.
If you go with the fabric paint method, you want to make sure it's not the puffy kind, and you want to follow the instructions on the paint bottle for how to set the paint so it won't fade in the wash. Here are some instructions for using a stencil and fabric paint, and here are some instructions for making simple shapes and patterns.
I don't have fabric paint, and I'd hate to buy some when I have so much acrylic paint in the house. From what I found poking around the internet, you can use Golden GAC 900 to modify acrylic paint for use on fabric. Then follow the instructions on the bottle for heat setting.
Very similar to the fabric paint method, though perhaps not as kid friendly. Here are instructions for using a stencil and spray paint, and here are some more simpler instructions for kid designs. The first set of instructions tells you how to heat set the paint so it won't fade in the wash.
This is by far my favorite design method since it seems the easiest and possibly the most cost effective since most people already have bleach in their homes. Though, again, you have to question the kid friendliness. Here are instructions for using a stencil, instructions with simpler stencils, and another set of instructions for basic shapes and letters. Though, I think my favorite method is the lady's pictured above, She just dipped a paint brush in bleach and hand painted the letters.
Tie Dye & Watercolor
Tie dye was a lot of fun when I was a kid. So this is definitely something you could and should do with your children. But keep in mind that to do something like the image above, you are going to have to tie dye the shirt and then use one of the other methods above to put a design on it.
OR you can use a t-shirt transfer (that method I mentioned I didn't like) and transfer a pattern you want to the shirt before dying. The dye won't be able to soak in to the fabric with the transfer. For simpler patterns this link recommends using Elmer's glue (a third of the way down the page under "Alternative Resist Methods").
If you do either of those resist methods (glue or transfer), you'll want your bindings on the shirt to be lose-ish for maximum color saturation. The girls in the photo tied theirs tight so they have a lot of white still, which means your resist pattern won't be as noticeable. Kids usually can't get their shirts that tight (if you let them do it themselves). But teens or adults certainly can, so it's something to keep in mind.
Here's tie dye instructions, and additional instructions for other patterns. If tie dying seems like a lot of work, you can also use watercolor paints to achieve an similar look. Here's how to set tie dye when you are done (the watercolor instructions explains the heat setting process). Wash cold.
You can use sharpies or fabric markers. You will want to heat set the designs, and wash cold.
This is probably the cheapest method (all you need is a shirt). But it might not be the easiest, and you have to have an undershirt to wear it with. Here's instructions (you don't have to do the sewing part) and here's some more.
Okay, so all these different t-shirt methods are great, but what kind of design should you use? For starters, take a look at other Bernie shirts out there. See if there's any designs you might want to imitate or combine. Check out the Bernie graphics reddit mega thread. And here's some Bernie stencils you can use. Go with the classic Bernie logo or get creative with freehand (#feelthebern).
I hope you find this helpful. If you read this post and make a shirt, leave a comment and if you can attach an image of your shirt. I have a trip to the Salvation Army I've been meaning to make, so I'm going to jump on the #diyforBernie bandwagon too. Let's see what fun creations come out!