I may be able to get my answer to this the next time I'm home, but it's nagging me currently. It was a trilogy in paperback, released by 1998 because I remember seeing them up on my brother's shelf after I took over his room, which was prior to my graduation from high school. The front cover shows a young man in greyish camouflage fatigues, I think with two swords across his back. I only got partway into the first book before I set it down for reasons I don't remember, but the main character is a young man whose parents disappear. He finds a note, I think from his father, explaining that they are actually royalty from a fantasy realm and where the portal to said land is (I think) in the back of a closet in the house. Said young man starts to understand why it is that his parents had him doing so many anachronistic activities such as swordwork and archery. He arms himself (I remember him picking up swords, a bow and arrows, and woodland outfits, which he notes are in the closet in both camouflage and "Robin Hood green". He may have also picked up some guns). After he goes to the other world, he at one point freezes and notes that the key to avoiding motion when hiding in the woods isn't to hold your breath, but to rather breathe slowly and calmly. That part made an impression on me as a teenager for some reason.
I don't remember much of what happened after he traveled into the other world. I have this vague memory of him meeting someone at a ruined building, but that's pretty much it.