It's ironic that after all the years of being with women and talking about having babies, turkey basters, the whole nine yards, that when I finally do get pregnant, it's with my male partner and we still used AI.
He's unable to ejaculate during intercourse so he'd masterbate and then fill up a syringe and ummm fill me up. Pet/farm supply stores are a great source of cheap syringes (you really don't want to use a turkey baster!). Make sure they're untreated (most are). You want the kind used to give oral medicines and such. In case it's not obvious, no needles!
We found that 3cc was the best size. 1cc meant filling it twice. 2cc was okay but borderline. 5cc and up worked but why use anything bigger than you have to. Rinse after use and rotate them so the one you use is bone dry (water can kill sperm). Throw them out each month.
I highly recommend Toni Weschler's book, Taking Charge of Your Fertility. We inseminated every other day starting from when I first had fertile cervical fluid until ovulation. Full timing instructions are in the book. We generally did this 3 times per month.
He felt for my cervix first (it's a good measure of fertility as well) and aimed the goo as close to the cervix as possible. I had my hips up on a pillow and my legs bent, and lay on my back for 20 mins or more (or until I got too bored). That part isn't considered strictly necessary (it's definately not necessary for intercourse insemination) but it doesn't hurt and it's commonly done.
It took a year to get pregnant (about 10 months of trying since we skipped a couple). The fertilitity doc I started to see said she's seen poor results with home insemination but that doesn't match the results my friends have had and I honestly don't think she could do a better job if it's just an ordinary vaginal insertion.
I think it took a long time because I'm 40 years old, have a bunch of medical problems, and my partner's sperm wasn't as good as it could be (though it was mostly okay). But who cares why? I'm pregnant!!!!
I don't mind answering pretty much any level of detailed question. The instructions I had to go on were somewhat vauge and it was hard to figure out some things.