It all depends on how complicated the linkage is. For many simple linkages all you need to know is trigonometry (sin, cos, tan) and torque/moment equilibrium (Force x Distance = Force x Distance). Once you can do this I would say you are in the 95th percentile of linkage design ability. Most non mechanical engineers do not have the ability to calculate or visualize the force transmission of a simple linkage.
If you want to get better and design more complex systems you will need physics 111 and 112 (calculus based). Calculus 1, 2, and 3 are also necessary, mostly 3 because it involves vectors. Statics and Dynamics (200 level engineering courses) tie everything together and reinforce the academic rigor to reliably calculate mechanisms. Machine design (300 or 400 level engineering courses) teach how to add in dynamics, strength of the linkage, inertia, how to simply complex gear systems, optimization, etc.
There are lots of good physics, statics and dynamics books. Probably have a look through a local college bookstore and see what they have (i usually just got the isbn and bought mine used on half.com to save $). Or visit with a professor; they may be able to give you an old copy or point you in the right direction.
Once you have a good trig and physics foundation I would recommend Shigley's Mechanical Engineering Design and the Mechanical Engineering Reference Manual.