Fabric paints need to be heat set if they're painted on something that's going to be washed. The process is the same as ironing a garment, except you'll iron an area for longer than you would to iron out creases, and you shouldn't use any steam. Set the iron on a medium to hot setting, then run the iron across the painted section of fabric for a few minutes, moving around constantly so you don't scorch the fabric. If it's a delicate fabric, set the iron to a lower, suitable temperature and iron for longer.
Remember to turn off any automatic steam settings if your iron has one, or empty the water container. You want dry heat for setting the fabric paint.
If feasible, iron on the 'wrong' side (not the painted side) of the fabric, or alternatively place a 'scrap' piece of fabric over the top of the painting (an old, thin dishcloth for instance). This helps protect your iron from any transfer of color before the paint is heat-set, and accidentally scorching the 'right' side of the fabric. You might also want to put a piece of fabric down on your ironing board to protect the cover.
How Long Should You Iron Fabric Paint to Set It?
My rule of thumb is to iron for "not less than two minutes, ideally more". Golden Paints recommends ironing "for 3-5 minutes with a medium-hot iron on the reverse side".1 Be careful as the fabric will get quite hot to touch. I iron relatively small sections at a time, as then it's easy to move the iron around fast enough that no part cools down too much but likewise no part gets so hot it scorches. It's definitely not the exciting part of the fabric-painting process, and I tend to do more like three minutes than five, but I motivate myself by thinking about how disastrous it'd be if the fabric paint washed out or ran! So far nothing has though. If in doubt, rather iron some more.
I usually wait 24 hours after I've painted something before heat setting, just to be sure the paint is dry. Then several days after heat setting before washing it. Golden recommends "at least 4 days"2.
If the paint is completely dry, there shouldn't be any risk to your iron. If there's still some wet paint somewhere, then if you iron over it, it'll dry with a ffsssst noise (almost guaranteed to make you jump the first time it happens!) and will probably stick onto your iron. You should be able to clean it off, but prevention is easier than cure so either wait until you're completely sure the paint is dry, or use a thin cloth between the painted surface and the iron. I have a basic, old iron I keep just for crafts, so I don't have to worry about it too much. It's boring white and I definitely don't adore it, but we've had a long working relationship...
1&2. Golden Acrylics on Fabric, accessed 26 July 2010.