Go get a regular brake bleeding kit for about $10 at any auto parts store. You can't pump the lever to build up pressure, all that is doing is applying pressure, then relieving it, and then applying the same pressure again. The idea is to pump brake fluid through the lines to push out the air bubbles. The bleed kit should consist of a rubber fitting for the nipple, a clear hose, and a little cup for the hose to go in. You need to put brake fluid in the cup and make sure the clear hose inside stays submerged. You will most likely have to hold the cup because the clear tubing usually forces the cup to sit however it wants to. You need to put the tightest nipple fitting on the nipple that you can get on there. The kit usually has multiple sizes. Make sure the fluid reservoir is full, and then loosen the nipple on the caliper just barely enough so that you can squeeze brake fluid out when you pump the brake. Whenever you release the brake, it will suck fluid back in through the nipple, which is why you need to keep the clear hose in the cup submerged. Keep pumping the brake until either you don't see any more bubbles in the clear hose, or the reservoir gets low. When the reservoir gets low, hold the brake lever in and tighten the nipple to close it again. Refill the reservoir. You will most likely have to keep emptying the cup too, so have something ready to dump it in when it gets full. When you don't see anymore bubbles coming out of the nipple, tighten it up good. I would recommend using the closed end of the wrench and just set it on the nipple even before you put the rubber fitting on it, then just use the wrench as an "open/close" lever. Bleed nipples on calipers are probably the easiest thing on any vehicle to strip, so make sure it's the exact size wrench and don't use the open end.
Do this to each caliper and then you need to do it to the master cyclinder on the brake lever. try not to get any of the fluid on painted surfaces, and if you do, clean it right off. If the nipple fittings in the kit don't fit well, you can push the loose fitting against the nipple while you have the nipple open, and have someone else pump the brake for you. It might take longer to do it that way because you still might get a little air sucked back in every once in awhile, and some fluid may come out. It will get messy either way, so have quite a few rags or paper towels.
Just for future reference too, the rule of thumb to bleeding multiple components in a brake system is to bleed the furthest one away from the reservoir, and work your way to the closest, hence, bleeding the calipers first and then the master cylinder. I don't remember if the brake lines to the calipers are the same distance or not, but I'm sure the difference in hose length wouldn't make a difference in this case.
Now that I think about it, the bleed kit might not have the fittings and just has you put the rubber hose directly on the nipple, which is fine. I think it'll actually make a better seal. It's the vaccum pump kits that have the fittings on them, and I've tried to use them a few times, but like someone else said, you get better results from just doing it the manual way.