How early should I show up to class?

Honestly, sometimes it really doesn't matter how early you get there because the professor might not be in yet, but I would personally suggest getting to class about 10-15 minutes early so you can find a good, comfortable seat. Try not to get the seats in too far back so you're considered to be part of the "late crew" that just strolls in, but don't be too eager to sit in the front if you're not one whose prepared to randomly be called on to answer something. No matter what, avoid being late, and if it happens - try not to make it a habit. Even if the professor doesn't know your name, they'll surely know you as the late one by the end of the semester and let's just say that might not work favorably if you try to visit during office hours about grades. On time is late, so be there just early enough to find a good spot, and maybe even get to know someone in class!

This really depends on how many students attend the course. 

In a class with a lot of students, I like to get there 10-15 minutes early to get a seat and socialize with friends. In a smaller class setting, 5-10 minutes should be sufficient considering you probably won't have to fight for your seat.

However, it is always comforting to know that one has time to relax before class, so it depends on your comfort level in the course as well.

I work with a lot of college students - both successful and not-so successful ones.  I find the successful ones arrive early and sit up front.  The upfront view allows the student to avoid distractions, get access to the professor or TA early once class ends, and can help if you are getting lost in a lesson.  The back row is too easy to fall asleep, play online, or bolt out early if a tempting offer for fun comes in via text.  Want to do well academically and not waste $? Go to class!!!