Basic ratio is 1 cup of Kosher salt to 1 gallon of liquid. I use that ratio with apple juice or cider plus some orange zest, peppercorns, and a little honey. Heat it up to dissolve the salt, then chill it in the fridge after it comes back to room temperature. An 8 hour soak for the turkey is typically good.
When it's done, take the bird out of the brine, pat it dry, and let it sit out for a bit to dry off more before cooking. Not too long, though. It's still poultry.
The trickiest part is finding something big enough to hold the turkey. I've brined them in coolers, fermenting buckets, and meat tubs. I even found a pack of gigantic ziploc bags at the store that will hold a typical wild turkey. Those worked great until I couldn't find them anymore. If you have a container that you can fit in your fridge, that'll be easy. If not, brine it in a cooler and keep changing out frozen 2 liter bottles to keep the brine cold. This will also help raise the level of the brine to keep the turkey covered.