Vintage and antique gold-rimmed glasses are very beautiful and can be delicate. Do not clean them in the dishwasher. Place a towel in the bottom of the sink and gently hand wash. Add a splash of vinegar in the rinse water for extra sparkle. Hand dry with a soft towel.
In order to learn the value of your glasses, you need to do some research. Many companies have produced gold-rimmed glassware over the years. Are the glasses made of glass or the more valuable crystal? Gently tap the glass. If it produced a nice ringing tone, it is probably crystal.
You can learn more about your glasses by checking out some books:
"Crystal Stemware Identification Guide" by Bob Page (from Replacements Ltd.)
"Florence's Glassware Pattern Identification Guide" by Gene Florence
Once you are able to identify your items you can search for similar items online. You can try Replacements which will suggest a retail value (not always what you can actually get for the glasses but how much they would cost retail). Look for your glasses at online markets like eBay, Ruby Lane, or 1stdibs. On eBay, look for the amount paid for completed sales which will show what someone has actually paid for the product. Remember that asking prices can be greatly inflated.
You can also post images of the glasses at an online antique forum.