You want to remove the wheels, seat post (you may be able to get away with setting this all the way at the bottom or doing nothing depending on how you're storing it), handlebars and pedals. If you can go to your local bike shop and get a (cardboard) box for shipping bikes, the bike should pack in nicely for storage. This video shows you the steps in a nice way visually. You're not shipping it, so you don't need as much bubble wrap and straps and foam, but bubble wrap is nice.
The tools you'll need are likely a set of metric hex keys (mostly 5 mm, possibly 4-8 mm) and a thin adjustable wrench (maybe a pedal wrench too).
To remove the wheels, you likely have quick release wheels, so just pop the lever and unwind it. Undo the brake's quick release and the wheel will come out. Be careful not to let the derailleur get impacted as that can make it come out of adjustment (e.g. don't drop the bike when you have the wheels removed).
The seat post will be either a hex key or quick release. If its a hex key, try the appropriate size hex key (4-8 mm). If its a quick release, pop the lever and unwind it. If you're not using a bike box, I'd stuff the seatpost with a bit of newspaper or something in case critters make a home there. The seatpost is also likely to be greased, so wipe it clean.
The handlebars should be removed and put to the side of the bike. I wouldn't disconnect any cables.
Simply remove the bolts on the front of the stem (the four bolts on the front of the red piece, in this picture), put the handlebars to the side of the bike and re- attach the red piece (so you don't lose it). You may want to tape them to the bike to prevent them from moving.
For the pedals, you'll either want a thin adjustable wrench which can adjust to about 15 mm or a pedal wrench of the appropriate size (a combo 15 mm + 9/16" will be fine). Note the left hand side pedal (when you're riding the bike) is counter threaded -- that is, it tightens counter clockwise, rather than clockwise. The right hand side pedal tightens clockwise. Remove the pedals. Wipe the pedal threads and crankset eye clean.
This should all fit nicely into a bike box which would be ideal for storage. Gloves may be nice for preventing your hand from getting messy. To re assemble the bike, do this in reverse, making sure to grease your bolts + pedals + seatpost appropriately.