Just keep trying. It doesn't get any easier, but you'll go faster. The biggest thing is to make sure your saddle is the proper height for full leg extension so you don't damage your knees. In a few weeks you'll probably have increased the miles enough to notice the benefit of slick tires.
Your bike doesn't actually have 24 gears, more like about 12 with some that repeat themselves. Changing the front chainring is like jumping two or three gears in the back. Start in about 2 in the front and five in the rear, go up to 3 in the front for downhills and down to 1 in the front for uphills and fine tune your cadence with the rear. As you get stronger you'll probably be pushing bigger gears, but you need to start somewhere.