We just moved here about 6 months ago, so I can tell you what I have found so far - but there is so much more available for homeschooling than I'm used to! First, let me say that I moved from one of the most restricted homeschooling states, to NE, which is on the opposite side of the spectrum! I had to complete a questionaire (mostly about me and my education, my experience teaching), and have a couple forms notarized (saying that yes, my DH and I want to homeschool, and that I am 'the principal'), as well as provide some basic information about hours/curriculum. But I have nothing else to submit - no portfolio nor any required testing. There are two options for homeschooling - one is a religious exemption, the other is a non-religious exemption.
There is a very large Christian homeschool population here - some churches have their own groups. Omaha HEN (see above post) is the largest Christian group - and is community wide. There is also a secular group - Nebraska Secular Home Educators (NESHE). There is also a separate Homeschool High School group. Many homeschool-specific opportunities in and around the city - band, orchestra, theatre, sports, Boy Scouts, American Heritage Girls, 4-H,... Also lots of great learning opportunities here as well - fantasic zoo, children's museum, local/area history museum, botanical garden, great hiking in state parks, lots of local parks/playgrounds/pools, HUGE library system....
Hope this helps! If there is something specific you'd like to know, I'd be happy to try to answer!