To see if your GW plan will cover it, it's best to check with them directly -- if your private coverage is provided by an employer, they will have negotiated certain things to be included or excluded to keep premiums (for employer and employee) to a level that they are happy with. So, it's possible they will cover some, part or all, depending on the coverage you have. I would suggest getting your plan booklet and reading through and if you aren't able to get the info then call up GW with your plan number and membership number and ask them directly - I dealt with GW a LOT in my job and they are very helpful!
If they do cover it, what you will need to do is get a prescription for it, and send a copy of the prescription to them with your first claim. You will have to have the script filled at the pharmacy rather than buying it off the shelf, and keep your receipts. Then there may be a portion that you have to pay and a portion they pay (for instance they may pay 80% of the cost up to a maximum per year) but this will again depend on the specific coverage that has been negotiated in your plan.
HTH!