Basically, you want to "take in" the side seams.

As a newbie, you should probably experiment on one of your older shirts that you don't like to wear because of the problem. One that if you mess it up you won't really care.

You'll need some thread, a needle, a seam ripper and some pins. A sewing machine would be a little faster, but is not necessary for this job. The thread should match the shirt for a finished product, but for experimenting, it will help you more if it contrasted so you could see it. This first one is for practice so you'll get it right on one of your newer shirts that you really like. Once you have these things, you're ready to start.

Try on the shirt. How much too big is it? Pinch in how much you want gone on each side. Let's say that it is 1 inch on each side at the bottom. Remember your measurement. How far up the sides is it too big? Put a pin where it fits you fine. Don't stick yourself!

Take off the shirt (carefully!) and lay it flat INSIDE OUT on a hard surface (Not the bed, you'll end up pinning the tshirt to the bed). Measure in from the stitches at the bottom how much you want gone. Mark it with a pin.

What you'll want to do is pin the front to the back in a few places along the new seam line so that the t-shirt won't scoot around while you sew it. You'll be sewing a line from the pin mark at the bottom to the place where it fits right. Use a backstitch and try to sew as straight a line as you can. A wiggly seam will make the shirt look kinda puckery on the outside. If the t-shirt scoots you'll have a bigger pucker. Since this is t-shirt knit, don't pull your stitches real tight. That will make it puckery too.

If the bottom is 1 inch too big, and the shirt fits fine across your bust, then you'll have two seams (yours and the original one) that look like a long upside down V with the pointy part of the V at your bust, along the edge of the shirt.

Once you sew one side, try it on again and see what it looks like. The do the other side and try it on again.

Make sure you can still take the shirt on and off! You CAN take in the seams too much. :-)

If the seam is all puckery, look at your sewing line and see what went wrong. You'll probably have to use the seam ripper at some point, but don't give up. You'll get the hang of it, and that's why we started with the old shirt. Seams take a little practice and so does working with the seam ripper so that you don't put a hole in your fabric. That still happens to me occasionally and drives me nuts.

Once you like the results, if there is a big flap of fabric in the seam (inside the V) you can trim it off. Knits don't ravel out so it'll be fine. Just leave about 1/4 to 1/2 inch outside the seam, so your seam doesn't pull out when you take the shirt on and off.

Good luck!!

Here is a link that might be useful: How to do a backstitch