Have you studied Lagrangian mechanics? If not, you should study an introduction to this.
You probably should read the short, excellent book A Traveler's Guide to Spacetime: An Introduction to the Special Relativity by Thomas A. Moore. After this, start reading Gravity: An Introduction to Einstein's General Relativity by James B. Hartle,
https://www.amazon.com/dp/0805386629/?tag=pfamazon01-20.
Also, read right now the following paper by Hartle, a professional relativist, on his perspective on how general relativity should be taught:
http://arxiv.org/PS_cache/gr-qc/pdf/0506/0506075v2.pdf.
Even though I am interested in some of the more mathematical aspects of general relativity, I strongly agree with Hartle that tensors and differential geometry can wait until after substantial familiarity with general relativity has been built up (section V in the paper). I think this is particularly true for folks learning general relativity by self-study.