The simplest slide rule is just a number line with a movable pointer. To add 2 numbers, x and y, simply place the marker on x and move it y places to the right.
To subtract y from x, place the marker on x and move the marker y places to the left.
Slide rules become much more useful when paired with logarithms. As you should know, to multiply powers with the same base, all you have to do is add the exponents. For example, to multiply 23 and 24, all you need to do is add the exponents, 3 and 4, to get 27 (which is 128). Conversely, to divide powers with the same base, simply subtract the divisor's exponent from the dividend's.
In the slide rule below, the powers of 2 are marked above and the corresponding logarithms (base 2) of those values are below.
Now, if you want to multiply 2 powers, say 16 and 32, then you just have to add their logarithms, 4 and 5. So all you have to do is move the cursor to 4 and then move it 5 places to the right. The cursor will land on 9 and its corresponding power, 512, which is the product of 16 and 32.