I have found a few papers that do a good job explaining the basics of F-theory in a relatively easy way. I could have posted them as un update of the previous post on the subject but I think it deserves an small separated post.
One paper is : F-theory, GUTs and Chiral Matter.
Another one, written by Hackman and Vafa is: From F-theory GUTs to the LHC
Also I think that the interested reader would try to understand more basic settings, previous to the F-theory revolution. I am talking about the intersecting branes scenarios. A short and good review is: Progress in D-brane model building.
The reason to investigate the last paper is that I find it is interesting to understand how one calculate family numbers, how chiral fermions arise and so that in more conventional D-brane models. In fact the firs paper I cite makes a good job explaining some of that aspects, but still.
Also I recommend, once again, the original paper of Ibañez, Quevedo et all in local models D-Branes at Singularities : A Bottom-Up Approach to the String Embedding of the Standard Model. I have finished to read it and I find it very clear. As a plus it also has a brief chapter about F-theory.
Certainly the last papers about D-brane model building are not required to understand the F-theory ones, but It is good to understand what existed previously to better understand the goodness of the new. In that sense the papers recommended in my entry about the prehistory of F-theory GUTS are also valuables and focuses in diferent aspects than the ones cited here.
Anyway, if someone only wants a quick, but accurate, idea of the subject the two papers cited at the start of the post make a wonderful work