One of the most useful products for simple wood-repairs is a simple wood-filler. Once dry, this filler can be sanded and painted.
For a nice wood project, solvent-based wood patches or fillers are recommended. Some of these products are made with actual wood material, so they stain like real wood.
If you're going to be staining your project, make sure that the filler you use states on the label that it is stainable. Some fillers, though not stainable, are pre-tinted so you can select one that matches the wood you're working with.
For larger holes or gouges, you may need to used one of the plastic-based fillers. For replacing a section that has rotted, use a rotted-wood stabilizer.
Aside from wood fillers, you'll need to decide what type of wood-stain to use. Oil-based stains provide a great look, but cleanup can be messy. Water-based stains are simpler to use, but are typically not as durable as oil-based.
Gel-stains are a good choice for beginner projects as they are relatively simple to use and forgiving in their application.
For small touch-ups, consider using a wood-finish pen.