Find the closest data points to the point you would like to have measured. For example, you could have rainfall measurements from Denver, Colorado Springs and Fort Collins, along with Boulder and Greeley. To project the measurements to Longmont, you would use the data from Boulder and Greeley.
Sort the data you have into dependent and independent variables. For example, you would assume that the rainfall depends upon the position, so rainfall is the dependent variable and position is the independent variable.
Calculate the linear relationship between the data points. For example, if Greeley -- the starting location -- has 17 inches of rainfall, and Boulder -- 50 miles away -- has 25 inches of annual rainfall, the linear relationship between Boulder and Greeley would be ((25 - 17)/50) x distance + 17 = 8/50 x distance + 17. You can check this by putting in the two distances. At 0, the location of Greeley, the equation gives an answer of 17, while 50 miles away, in Boulder, the equation predicts 25 inches of rain.
Find the independent variable associated with the point you you want to interpolate, plug it into the equation and solve. For example, Longmont is 30 miles from Greeley, so the equation that projects the measured rainfall to Longmont would be (8/50) x 30 + 17 = 21.8 inches.