Rivers, lakes, and other bodies of inland water are generally where the water table intersects the surface (there are exceptions, such as desert playas).

Precipitation lands on top of the landscape and percolates downward through any soils. When the soil is saturated, the water moves laterally (get a sponge and pour water on it until it runs off; the same principle is at work here). The location of the saturated area is the water table. When the saturated level rises sufficiently to intersect the surface, it shows as liquid water. If there is a slope, it will flow downhill as a creek, stream, or river (depending on the amount of flowing water). If the water hits a steep drop, it will form rapids; a vertical drop makes for a waterfall. Water in a depression will form a pond or lake.

Areas with thin soils or other soils that can't hold much water (like clay) will tend to have highly seasonal flow patterns that match the rainfall. Areas with thick soils rich in organic material can hold a lot of water and release it more slowly. Evaporation is a critical component of equation, too. The roots of plants tend to hold water in the soil, but the leaves tend to remove it. So to answer you question about rainfall, I recommend that you look at English weather. The Scottish highlands, for example, were pretty much scraped clean in the last Ice Age and there isn't much good soil there except in some of the valleys. Forests tend to congregate in the valleys where there is soil. The south of England has fairly good soils and rainfall, so trees often grow all over the place (except, again, in some of the thin soils over chalky regions).