I'm not going to get into the legal aspects of it because I think the pps covered things well.. The Essential Guide also has plenty of example contracts you can use as a basis for using a known donor, btw. I second the recommendation for that book, it has SO much information!
Anyway, we used a known donor, someone who DP has known for almost 20 years. In our case it was a little different, they made a subtle offer that DP and I thought about for awhile. We then first approached donor's wife (who DP has also known for the same amount of time) with the actual question, "Would you guys be willing to help us create a child?" We approached her first because we felt that it was important that she be behind the decision if he did say yes, and wanted to let her absorb what that would mean before taking it any farther. She was very receptive to the idea and decided she'd like to talk it over with the donor herself first before *we* asked officially. We had them over for dinner several times without the subject even coming up (which was hard - DP and I were dying to ask but wanted to respect their feelings and wait until they were ready to talk about it), and when the donor was ready, he asked us to tell him why we wanted to have a baby, what our plans were, why we chose him, why we wanted a known donor, etc etc. To give him credit he also questioned me closely (as the one who would carry) about what sort of legal protection I was going to give DP and what I would do in the instance of a divorce. I think he wanted to make sure for his own reassurances that we had the right intentions, etc, and I am glad that he "checked into" our motives as carefully as he did. Anyway, he decided that he would donate for us. That part was a little funny and awkward, it seemed like my menstrual cycle was the topic of conversation for quite a while! The odds seemed stacked against us because every time it came around to "donating" time something woud interfere, either we'd be out of town, one month his entire family came down with the flu, etc.... anyway, we did perform a "practice" month, where he came over and left us a donation and we inseminated even though it was past my fertile time. We felt it was important to get the "heebie jeebies" out of the way so we knew what to do during the real thing. Oh, we also had a blood workup done on him as well as a full STD panel to cover our bases. Anyway, after the practice run, we got pregnant on the first attempt. However I just thought I'd mention that while it worked, we only had one "shot" that cycle because a couple different times we tried to get together to get the "donation" and things just didn't work out - I think the donor felt a little uncomfortable retrieving the supply while we were all waiting around for it, kwim?
When DS was born, the donor and his wife were the first ones to see him after he was born (besides DP and I obviously). The donor took his one moment of "proud fatherhood", checked DS's fingers and toes, etc... and then handed him over to DP as if to symbolize the handing over of his parental rights (that's what I felt at the time, it may sound corny but there you go.). He's actually only seen DS once since then because they moved out of the area. I think the donor is more comfortable not having much of a role in ds's life right now at least. I think he preferred to let DP establish her right as a parent without him around to remind anyone of his biological part in all of this. I'm actually kind of glad, because I think DP did suffer a bit from feeling "not as much" a parent - we went through a phase in the first couple months of ds's life where she was extremely sensitive to any comment that knowingly or unknowingly said anything about her not being a parent. She's overcome that now, especially since ds makes it perfectly clear he wants both of his parents around.
Whew that was more longwinded that I intended! I hoped that by telling our story it might help give some ideas what sort of emotional issues might be involved.