The hops will get kind of papery and lighter feeling. Sometimes you will see a few hops starting to brown, this is a good sign that there are hops ready to harvest. Also, they will smell very intense when ripe. Just go around and squeeze on some hops throughout the season and smell them as they mature. You will get a feel for when they are ripe.
Once you harvest, you can dry them a couple of ways. I prefer to use a dehydrator. I have one that can be set on different temps. You want to dry them on low heat. You can also set up some screens somewhere and run a fan over them. Just spread the hops out and don't pile them up too thick. It helps to turn them once a day and mix them up a little so that they dry more evenly. You want to dry them until the strig (the stem inside the hop cone) snaps when bent. The outside leaves can seem very dry and the strig still be limp, so be patient. Once they're dry, you can store them in vacume bags, jars, or whatever containers you want and then refridgerate or freeze them. I prefer to vacume seal and freeze mine.