I think the answer depends on what your state requires. If you need to keep track of attendance then I would get a small calendar that was for attendance and then just put a check mark on it for each day you "do school". That would likely be most days for an unschooler!
As far as records and portfolios, you have to be a touch more creative. We don't unschool but we are very relaxed and, up until starting to lapbook, tend not to generate a lot of "paperwork". So I used my digital camera A LOT. Anything that resembled a field trip would have picture taken at it. I take pictures of art work and anything else that is an activity. I store all the pictures in the computer and pre sort by subject and then by activity. When it comes time for the portfolio to be assembled I can go in and print one or two good pics from each folder.
We just joined an umbrella school to avoid all of that. Every quarter all I have to do is send in an email saying DS1 has attended 45 days this quarter and DS2 has attended 45 days this quarter. I still keep all that stuff but I don't feel the pressure anymore, LOL.