Nebraska is shall-issue and are issued at the state level through the state patrol. Here is the link to the NSP's website on it:
http://www.nsp.state.ne.us/findfile.asp?id2=252.
A course, about 8-10 hours long, is required to obtain your permit. The course is mostly classroom time, along with a written and practical/target shooting portion. Most classes seem to run $100-$150 in cost. You also have to pay $100 to the NSP for the processing fee. Many instructors also provide instruction for FL and UT permits which are handy if you ever plan to travel out of state. Once you pass the class, you must go to a state patrol office to be fingerprinted.
If you are east of Kearney, and particularly in the Lincoln or Omaha areas, you shouldn't have much trouble finding a class. Three instructors I can recommend are Chris Zeeb, Paul Horvick, and Devon Crinklaw. All three are well qualified but bring their own unique perspective.
Our sister site,
www.ccwne.com, is a bit more focused on CCW, but all of your questions should be able to be answered here.
