Vintage/Thrift Fair on Campus
First, you need to check the tag when you get it. If the tag is still attached, it will give you important information about the materials used in construction and washing/drying procedures. If there is no tag, just use your best judgement. Don't go washing a dark item that has no tag with lighter items because it might bleed. Don't put an item with delicate-feeling fabric in the dryer on high.
Secondly, you need to go about actually washing things. There's no reason you can't toss things into the wash with your regular laundry, just so long as you're combining things that need to be washed similarly. Do a once-over of all of the clothing and look for stains, applying a stain-remover as needed. If it's in a thrift store, unfortunately, some of the stains may be really stuck in there, so be liberal with the stain-remover and do a bit of scrubbing. Then, wash according to the tag instructions. If you're really bothered by germs, wash on a higher temperature to get yourself rid of anything particularly nasty.
HOWEVER, if you picked up something really vintage, you'll need to do some handwashing rather than putting it in the washing machine. Avoid using a strong detergent and stick to a mild one, such as ivory soap. Dandelion Village, a vintage retailer, has a blog which contains a guide for washing vintage clothing which I have found particularly useful, link to part one here and part two here.
Now is the time, after you've done the washing, to alter your clothing. Try it on and wear it for a while. Walk, sit down, stretch. If you have enough sewing skills, you should be able to pin-point any areas you need to alter just from doing that. You can also make cosmetic changes to the garment, of course. One of my best changes to a garment was a simple swapping of buttons, because whoever decided that a purple shirt should have tiny gold baubles in place of buttons was out of their mind. Adding lace to hems, patches to sleeves, studs to shoulders, or any other number of DIY additions will really help and make your garment more you.
The matter of shoes and accessories is slightly different. If you've managed to find a pair of shoes, chances are they've already been cleaned by the thrift store. You can clean the inside with a soft, damp (not soaking) cloth and bit of mild detergent if you would prefer. A tiny bit of polish for any metal fixtures, and some leather polish can also improve them. If you're in love with the shoes and they seem good quality but the tread is worn down, you can take them to a cobbler to get a new tread put on, but I wouldn't recommend it for really cheap shoes.
Bags can be cleaned, again, with a soft cloth, or scrubbed if they're fabric and a bit dingy. You can also make changes to bags, if you like, such as replacing the zipper or other fixtures. Belts can be polished, but I don't know of any big DIY changes you could make to those (except maybe studding them or stringing a chain on it or something.) Jewelry is somewhat different. In a thrift store it can often be difficult to tell what is good quality and what will turn your skin green. Covering the parts of the jewelry that will touch your skin with a clear sealant can help (in the past I've recommended clear nail polish, but that's probably not the best solution. If you're stuck on options, Decoden websites have some great solutions for what kind of thing.)
Thrifted clothing can be stored like non-thrifted clothing. To combat any moths who might be out to eat your clothes, hang a sachet of lavender in your wardrobe. Finally, wear your "new" thrifted clothes, and enjoy!