I remember doing mine in a more major way when I was about 10. I just followed the rest,ice,compression, elevation (R.I.C.E.R) etc steps avoiding the heat, alcohol (of course not in a 7 year old unless he's French), running and massage (H.A.R.M). He can take something for the pain but it's best to ask your GP what he/she recommends as we don't have a full medical history. The main reasons healing time is shorter is better blood supply really although we are looking at a tissue that doesn't have a great blood supply to begin with. Remember that inflammation after injury is a healing mechanism and so whether to take an anti inflammatory agent is controversial. It helps with pain but not with healing. Maybe a mid pain killer is best in this case.
Basically After the initial 24 hours he can begin partial weight bearing using crutches if required. Gradually he'll progress to full weight bearing over several days as tolerated. I would strap him with a light compression bandage to permit him to use a normal heel-toe gait (walking pattern). As soon as pain allows, rehabilitation exercises should be done but if he is strapped well he should be able to bend the ankle forwards and backwards a little just not so much side to side.
As for taping this is probably not needed. Children's skin is also more sensitive so it might not tolerate the tape very well. He should be resting right now and time will heal but this is likely to be a few weeks. He should then be assessed for balance on that leg to see if any of his joint receptors have been compromised. If this is the case then he needs a more active rehab program but at 7 they are pretty active and so life itself at that age probably provide most of it.
If in doubt get some good advice from your local physio. Our comments should only be used as a guide and I am assuming he has been cleared of any fracture that can accompany an ankle sprain.