If you hire a steward for your house, you can buy lumber through him. This functions exactly the same way as buying it though a saw mill owner, 200 gold for 20 sawn logs.
In some mills it's possible to do a "quest" (More often than not simply selling them some firewood) that will raise their disposition towards you enough to let you cut your own lumber for free. This (obviously) has the plus side of being free - however, each cycle of placing the log in the machine, cutting it, having the machine reset and then getting your logs takes around a minute and only nets you 10 logs a time. Also, it seems like every time you leave and come back you have to ask him again or you won't receive logs, so you have to do it during business hours just like buying them from the owner.
So, if you're just starting out a new house, talk to a saw mill owner. If you're loaded with cash, get a steward and buy from him to avoid having to go at certain times and just hassle in general. If you're strapped for cash it's possible to cut your own for free from certain saw mills.
To see which mills you can cut lumber in, see this page: http://www.uesp.net/wiki/Skyrim:Cutting_Lumber
That same site also has basically any info you could ever want about any Elder Scrolls game, so it's worth a bookmark if you plan on playing Skyrim for a while :P
BF3 Platoon for Skid Loader lovers - The Skid Loader Club: http://battlelog.battlefield.com/bf3/platoon/2832655241192792365/