The Thin Lens
A thick lens is a little trickier
The Lensmakers Formula
The Radius of curvature for each surface determines the focal length.
Where :     f = focal length
                n = index of refraction   ( for most glasses it is 1.5 to 1.7 )
                R1 = radius of curvature for first surface the light will hit.
                R2 = the other side of the lens' curvature.  ( note: the radius can be negative in the case of concave surfaces)
This diagram shows our Thin lens with an object (blue arrow) to the left, and the image it forms to the right.  Notice the Ray Tracing ( red lines ).  Here this is a visual aid, but in the Olde Days, it was a valid method of designing Optical Systems.  Some people still use it today.   To Ray Trace, do the following:

1. Mark the Focal Points (F and F`) of the lens, for a Thin Lens it is the same distance (focal length) from either side of the Vertex (the center of the Lens).
2. Start from the top of the Blue Arrow Object, and draw a Parallel Line (parallel to the Optical Axis Line)  to the Lens, now turn the line to pass through the Focal Point, F' and continue on a little ways.
3. Start again from the top of the Blue Arrow Object, this time go through the center of the Lens where it crosses the Optical Axis, and go through to connect to the first line.
4. Lastly, start at the Blue Arrow Object, go through the other Focal Point till you get to the lens.  Now turn and go parallel till you intersect the other two lines.  This is where the Blue Arrow Image forms.

Now for the Equations
   
m = magnification