Question
The soil in my backyard is eroding... possibly from rain.  Where do I start to determine and prevent the problem?

Answer
Soil erosion is caused by an interaction of four factors.
1. Agent: Usually water or wind; and heavily dependent upon the rate of flow of either one. I will assume that you are dealing with water from rainfall.
2. Soil-particle size: Generally the larger the soil particle (sand) the less it will erode (move) compared to a smaller particle (clay).
3. Soil porosity: The ratio of air to mineral and organic solids in a given volume of soil. The more air space in the soil mass, the more water it will absorb (like a sponge) before runoff begins. Runoff occurs when "The rate of precipitation exceeds the rate of infiltration". The rain is falling faster than the soil can absorb it. Runoff will gather speed as rainfall increases in intensity or duration (inches of rainfall per hour) . A light drizzle lasting many hours can record the same total as a short heavy shower       
4. Slope: The steeper the incline or slope, the more quickly water will flow and the greater will be the erosion.
 We can intervene in a very limited way.
The amount of rain that reaches the ground can be reduced by a crop - trees, shrubs etc.
If the precipitation cannot be intercepted, then a layer of absorbent material (mulch) will act as a 'sponge' to delay runoff.
If this proves to be inadequate and slope is a significant factor, then placing barriers across the slope (palm trunks, railroad ties and the like) will eventually create terraces. The barrier will slow down the rate of flow and cause the soil to be deposited. The effectiveness of this technique depends upon following contours - a line joining points of equal elevation.
Then there are 'French drains'; and flexible perforated plastic pipes with or without 'blankets' which are used to channel the water away and dispose of it competently.
If this all sounds intimidating, it is; in proportion to the  extent of the problem.
Come back if you think that I can help. The Engineering Department of the City in which you live may have resource personnel who will help you with the problem.
Happy New Year!