I would advise everyone to have state ID as one of the todo items on their list when you arrive in the US. If you haven't already, read Why you must get a state ID. A state ID makes local travel much more convenient and saves you from carrying your passport everywhere. Losing your passport can get you into a great deal of trouble and unnecessary inconvenience.
That said, there are a plethora of websites out there that let you compare and reserve flights for your domestic as well as international travel. I would always recommend to check multiple sources to get the most competitive prices. A few general tips that might help you:
Always plan and book ahead of time
If you are getting a particular price don't wait as it would most probably be higher the next day
If possible try searching with flexible dates (~3days) as sometimes flying on Monday instead of Sunday can save you a lot of money
For local flights always try to travel as light as possible. Almost all flights charge you additional for extra bags
Be sure to print your boarding passes ahead of time to avoid long lines at the airport
A few good websites for comparison:
Kayak
Priceline
Google Flights
Student Universe
Travelocity
Expedia
Cheapoair
Also try checking if Spirit Airlines offers service in your area. I have found them to be a great way to travel since they are usually offering the most cheapest rates by a big margin. The catch with them is that they will charge you extra for almost everything. For example, printing boarding pass at the airport: $10. Checking in a bag at the airport $100 (Early check-in $40) plus not complimentary food or drink during the flight. That aside, if you are a student on a budget Spirit is the way to go. Pack your backpack, grab a water bottle and stuff to eat and you are good to go! (Yes you can bring outside food! and fill your water bottle after you pass security).