If I remember correctly - screw the eyelets into the back of the frame the same distance from the top (about 1/3 the way down) Ikea may have a map to show where to screw in the eyelets or look for marks on the back. If not, just measure exactly about 1/3 down from the top on each side and make a pencil mark as to where you want the eyelets to go.
To get started get a small hammer - be very careful not to split the frame or break it (!) - and tap the eyelets very gently, but enough to make them stick, to where you want to screw them in. Then take a pair of pliers (sp?) and twist them in until tight. This might take a bit of effort, and I found that if you twist the pliers with one hand and HOLD the eyelet with the other makes sure they get in straight. Make sure the holes of the eyelets are verticle when done.
Then, take the wire, loop it through one eyelet about two inches and twist the wire together to hold it in place. Then do the same with the other eyelet - being very care to leave enough slack for hanging, but not too much. If it is heavy enough, you might want to use two picture hanger hooks for the wall (that I believe you have to buy separately) so make sure you account for that.
I hope this explains it. I'm not a professional picture hanger, but was in the exact same situation with an IKEA frame once
Good Luck!!!
PS - or you can wait until someone comes home and get their help!