Even though Railgun is a spin-off from Index you don't have to watch Index before hand to know anything about what is happening in Railgun since it's an entirely stand along series even if characters from Index make several cameo appearances through out Railgun's episode arch.
So what is Railgun? This is what Anime News Network had to say about Railgun's plot.
Academy City is a highly developed place in terms of technology. It is said to be 20 to 30 years ahead of the rest of the world. 80% of it's 2.3 million residents are students. The focus of all studies here is directed towards esper powers. Misaka Mikoto, one of the top level espers in town, shares a room with Kuroko Shirai, another high level esper who is a member of Judgement, a law enforcing agency composed of students. Both attend to Tokiwadai, a private school reserved for the high-leveled and the rich. Kuroko's partner at Judgement, Kazari Uiharu, is a low level esper who studies at Sakugawa middle school. Her best friend and classmate there is Ruiko Saten, a level zero (no esper powers). Together, the four encounter several adventures in the exciting scientific town.
I just want to add that Railgun does an interesting twist to it's story telling. For one it's part episodic and part major plot the episodic tails often don't have anything to do with the main plot but are still more than interesting to keep it from seeming like a nuisance to the larger picture. Also interesting is that they made it feel like two seasons by separating the main plot into two different stories. Add in the odd swimsuit episode and you have a very different way of telling a story that I thought really worked well in the end. There is great character development and nothing seems like it's unimportant to the main story.
While most people probably like any one of the four main characters I personally like the glasses wearing side character Konori Mii (NSFW) who in the second part got a good couple episodes devoted to her.
I couldn't find a good trailer for Railgun so how about checking out the second opening.
