Well that depends. I'm an electrical engineering/physics dual major at college, so there's a lot I can tell you about this (warning: wall of text ahead)
Do you want to get into robotics and electronics as a hobby, or as a serious interest (ie consideration or pursuit of a career in electrical/electronics engineering?). Basically, do you want to just be able to build some cool stuff and neat projects, or do you really want to gain a detailed understanding of electronics (and make $80k+ a year, being the *starting* salary of an electronics engineer right out of college?
)
Arduino is a pretty good place to start if you have little experience with electronic hardware and physical devices. There are other great platforms as well (The Texas Instruments MSP430, and Parallax Basic Stamp come readily to mind) but the Arduino enjoys the most public support. It uses a very simple custom programming language, but as you progress you'll find it also works well with C/C++, and its assembly language instruction set is also made public (which can't be said for the MSP430 and Basic Stamp). The greatest benefit of the Arduino is that it and its add-ons ("Shields") are all open-source, as you progress you will find this to be a fantastic thing as it means you can construct your own add ons and Arduino board, a great money-saver and introduction into the world of electronics hardware design.
I recommend for learning Arduino in the context of an introduction into serious or at least semi-serious learning of electronics engineer "Exploring Arduino" by Jeremy Blum (which also comes with a coupon for a discount on a complete Arduino kit). It is not just an "Arduino book" (there are plenty of those), it uses the Arduino to introduce you to electronics engineering and it is a much easier read than many other texts on the subject. If you are just looking for projects, Instructables is a great website with a wealth of user-contributed Arduino projects available, although it's not the best way to go if your interest is in really learning electronics and robotics and project writers aren't great about documenting the requisite prior experience which can result in wasted money and in general being in over your head. I find that you will gain the most from Instructables if you already have a sound background in electronics.
But if your interest is more serious, as in, you are considering a career in electronics or robotics, there's a bit more you'll have to do:
Well, unfortunately, you're going to have to brush up a bit on your mathematics. A college electrical engineering program will come hard and fast with mathematics. Math is an integral part of electrical engineering regardless of what field you are in. Brush up on your basic calculus (I strongly recommend Dover's "Calculus, an Intuitive and Practical Approach") in particular, as the second semester of calculus is one of the big EE weed-out courses.
I also recommend Make: Electronics for reading. It will provide you with a hands-on approach to learning all of the core concepts of electricity and electronics.
If you have a bit more time to spare, I recommend signing up for the free online course platform Coursera, where an introductory course in electrical engineering ("Fundamentals of Electrical Engineering") is running right now, you can sign up free of charge. You will not be penalized in any way for starting late as the grade is based only on a single final assessment (Which does not open for 3 more months) and it's not for college credit anyhow. I am taking it right now and greatly enjoying it, even having much experience with the subject already, it's been a great refresher. It also does not require any prerequisites and is a very entry level course which will help you decide whether electronics engineering is something you might be interested in (it will also help out in any future courses you may take at school for the subject).
