Welcome to the Guild Katie! Well I'm not sure that I know of any programs that don't come with some form of learning curb, but the majority of members here use Photoshop or GIMP (a free to download bit-map program with much of the functionality of Photoshop), and most of the tutorials here are written for one of those two programs. However even if the programs themselves may take time to become proficient in, there are some great tutorials (in the tutorials section - I'd star with the Tutorials in PDF format sticky) that can help you learn to create maps in these programs even without having become completely proficient.
As for how to make a map look geographically realistic, well you may want to spend a bit of time up front learning about plate tectonics, continental drift and other related matters, as well as studying maps of the earth, before putting pen to paper (or bit-map, as the case may be). Learning about these matters will enable you to better think through what would count as a realistic looking set of land formations. You should also read the sticky on How to get your Rivers in the right place, which offers some sound geographical information. Now, as for the actual techniques of drawing these land forms, I'd check out the different techniques on offer in the tutorials section. To give you a sneak preview though, the two most widely used methods are either (1) to hand draw the land forms (either on paper and then scan it in to work on with a digital program - or use a tablet), or (2) to use vector clouds to create random shapes which you then manipulate to merge into land formations. Different techniques for this second method are discussed in various tutorials.
As to tips, well, I would recommend doing a bit of research before you begin. Spend time getting to know both the tutorials section and the finished maps section. The tutorials section will familiarize you with different map creation methods and the software needed to create them. The finished maps section will provide an abundance of inspiration that can help you to more clearly decide on the style you would like to attempt for your own maps. There are also some good discussions floating around on different aspects of creation. Once you are ready to begin, post up a WIP thread with a picture of your early map and ask for feedback. You will pick up more tips and tricks by gleaning from the experience of other Guild Members. Best wishes on your project.