Janet, I've done a bit of dyeing, even as part of my undergraduate degree. I'd try taking the stains out first, because dye doesn't necessarily cover up stains, it will absorb differently in those areas and go darker there instead, leaving you with an unwearable mess. I've successfully taken perspiration stains from silk using baking soda, but if you google that there are lots of different methods.
I heartily second the dharmatrading link as THE go-to place for dye. It is superior in every way to RIT. Silk is a protein fibre (as opposed to cotton, say, which is cellulose) and needs to be dyed with a dye for protein fibres. If you visit the Dharma site, you'll see a section for protein (silk, wool) dyes, so take a look at those. They even have Pantone colour of the season matches in their dyes, so it's a lot of fun choosing. You won't need much for a single blouse, so it will only cost a few dollars. They also have a section where they list detailed instructions for dyeing silk, so take a look at those. Be prepared to spend a few hours doing it properly, washing the blouse and having it wet before it goes into the dyebath.
One thing I've found with silk is that is sometimes loses some softness once dyed. It becomes a little stiff and less silky, with less sheen. If that's an issue, you might want to reconsider. ALso, thread used in sewing is often polyester, which will not take up this dye, so your thread will remain white. Sometimes that matters, sometimes it doesn't. If you have a lot of visible stitching, it might look odd. I find in that case it can be better to dye a pale colour so the stitching doesn't stand out much. The sort of dye that dyes polyester is nasty smelly stuff and I don't really recommend it as it isn't fun to use.
Good luck! It's very satisfying to dye things. I've recently dyed towels, a doona cover, various pieces of fabric and clothing and given them all new life.
