I'm in the late stages of recovery from a grade 3 last August (I probably completely destroyed some ligaments). The guideline I had was to stay on crutches until I could walk without limping, and keep the aircast on for some time after that, then only wear the aircast for high impact activity. I wasn't running without splinting until January, 5-6 months after the injury. Bad sprains take longer to heal than fractures and heal weak.
If your insurance and/or pocketbook covers it, there is NOTHING like PT. Had I gotten in sooner, I probably would have healed faster. The rest of this is stuff your PT or sports doctor would tell you, except they'll be able to tune it to you. What I tell you will be tuned to me
After the first couple of days, your priorities are (in order) range of motion, stabilizer strength, and weight bearing. Because of my specific injury, I found great improvement when I started wearing night splints to keep the back of my ankle from healing short. I still wear them. When I wake up in the morning, I spend a little while wiggling the foot around to limber up, then hop on the wobble board and do 20 circuits in each direction. That loosens things up for the day.
I used a bicycle inner tube for the ROM/light strengthening work. Loop it under the ball of your foot, hold on, press down and release slowly. 3x30. Then loop over the top of the foot to lift up, and a twist left/twist right. I put a few weight plates on the floor, stuck the bar into them, and girth hitched the tube around the bar to hold it at the correct angle. Then work up to balancing on the injured foot...then balancing with your eyes closed. Stand on a towel to make it harder. Finally you can work up to doing standing lunges, pressing off the injured foot. Running comes later, and go very easy to start with--I was stuck at week 3 of Couch to 5K for about two months. Bicycling is probably the best way to get your cardio. Lots of other exercises on the web.
Ice is good post-exercise. At other times, warm water baths may help to enhance circulation and healing.
Take it very very easy, "but take it," and good luck. Do not trivialize a sprain: it has the potential to be problematic for the rest of your life.