Over wifi it's easy, you can use the Files app to do it.
Make sure your computer is sharing some folders on the local network (right click>properties>sharing, or something like that)
Open Files>Shared Folders>add server>scan for server
It'll take it a second to find your computer, then you can browse the folder that you shared from your computer earlier.
I prefer an app called ESfile browser, though, instead of Files, it's a lot more full-featured.
To upload when you're away from the house will be tougher, but not too difficult. Zumocast should do it, but I've never used it. Other than that you could set up an FTP server on your home computer, which is what I've done. A guide on how to create an FTP server is outside the scope of these forums.
Sent from my DROID BIONIC using DroidForums
I also use DropBox; been using it for a couple years now. It's free up to 2gigs. I also recently signed up with Box. It's just like DropBox, but right now they're running a promo where if you sign up and install the app on your phone, you get 50gigs free for life. It's worth checking out.