As others have said Rit and another brand called Tintex are readily available. In many places they’re even sold in the grocery stores. Selection of colors varies widely. You can also order them online in bulk and get a better price and better selection.
I’ve done a lot of hand dyeing in my day so I’ll give you a few pointers.
First of all the fabric you’re dyeing with Rit/Tintex should be at least 50% cotton preferably 100%. That shouldn’t be a problem with most bandannas because they are usually 100% cotton, but not always. Check the label. If it’s not 100% cotton it will not be possible to get darker colors. You will only get a tint of the color on the box.
Before you dye the item wet it thoroughly. Many bandannas have a lot of starch in them and the starch can make the fabric take the dye unevenly so it’s even a good idea to use a little mild soap to get out all the sizing before you start. Rinse it well and then put it in the dye bath.
If you can get the liquid dye in bottles instead of the powdered in boxes, it’s preferable. It’s much easier to dissolve. If you can’t, the powder is ok but use the hottest possible (doesn’t need to be boiling or anything) water you can. MIX IT THOROUGHLY!!! It can take a while to dissolve. Rubber gloves come in handy for this. Swish the water in the basin around and make sure all the dye and salt on the bottom dissolves. There should not be any little flecks of dye left or you’ll get spots. Also, the dye powder can fly in the air and get in your nose so it’s not a bad idea to wear a surgical type mask when you do it. (unless you like blue buggers, but they aren’t too healthy for you!)
It’s a good idea to put a plastic under the area you are working in to protect surfaces and keep a wet sponge nearby to clean up any spills or loose powder. The dye can stain surfaces and be hard to get off even if you use bleach.
When the item is wet it will look like a much darker shade than it does when dry. The more dye you put in the bath the faster the color will develop. Let it get a bit darker than you want it because of this and because when you rinse it some of the color will inevitably rinse out.
Keep the dye bath as concentrated as possible but don’t overdo it. The more items in the dye bath the more dye you need. This seems like common sense but it’s the dye not the amount of water that makes a difference. There should be enough water to immerse the item you’re dyeing and not too much extra.
Don’t forget to wash the item after dyeing especially since you or someone else may be wearing it around your neck or head where you’re liable to sweat. It would be horrible to end up with dye rubbing off on your skin!
When you’re finished dyeing make sure you rinse the item to get excess dye out and then dry it. Drying in the dryer is preferable because if you hang it you may get streaks where the water runs down as it’s drying. If you use the dryer make sure you wipe it out with a rag dipped in bleach when you’re done to get rid of any dye residue or you may have an unpleasant surprise on your next laundry day. (If it’s your Mom’s dryer, I would ask for permission first!)
Wear clothes that you don’t mind ruining when you dye or wear an apron to protect your clothes. Any dye you get on your clothes is likely to stain permanently.
That’s all I can think of right now. Of course tie dye is fun and so creative! Don’t do what me and my friend Hilda did though. We made a bunch of things to sell at a boutique in Trinidad. Before she went on her trip she thought it’d be good to bring the finished Batiks to the dry cleaners. The dye washed out completely! What a disaster!
Just saw that a lot of this info is covered under Kardamon ‘s link tips for dyeing. Good link.