Plain t-shirts are simple to iron but have special problems because they often have printing and the material is usually very soft, thin knitted cotton.
You have to be careful of any printed front as heat will often melt the print and it will then spread over the t-shirt. The soft cotton often warps and distorts out of shape during wear and washing so may be difficult to get flat on an ironing board.
Here we have a typical child's t-shirt. It has a rubberized printed front and is distorted through the natural pulling a child does while wearing their clothes.
Turn the t-shirt onto it's back and straighten one sleeve starting at its bottom seam. Place the iron on the seam and guide it upwards at an angle holding the top of the sleeve slightly above the board, allowing any wrinkles to roll away. Then do the same with the other sleeve.
Now flatten the upper part of the body smoothing both layers with your hands and feeling for wrinkles on the lower layer. Iron up towards the top seam again lifting the fabric so any wrinkle can roll away. Always work out from the center either to the sides, bottom or top of the t-shirt.
Section by section work down the body always positioning the iron in the center working toward the edges. Keep using both hands to ensure you don't get any wrinkles caught under the iron.
When you've done the body flip over the t-shirt and touch up any areas that need it.
Make sure the iron doesn't go over the printing while you do this otherwise it may spread, ruining the shirt.
Some people prefer to iron t-shirts around the board, as if doing the body of an ordinary shirt. There is nothing at all wrong with this approach as the judgment of happiness depends on how comfortable you feel wearing it. However, by ironing around the board any distortions will be catered for and if you try to fold the shirt you won't be able to straighten the edges. The answer is to take whichever approach you feel is right for you.