The biggest thing is to make everything as clean as possible, to reduce the chance of infection. Clean sheets, scrubbed hands, sterile supplies, etc.
I used OPK's twice a day, starting 3 days before I expected to ovulate. We inseminated 12 and 24 hours after the first positive OPK, which also corresponded to the opening of the cervix (the os) being wide open, which indicates ovulation. Just for kicks, we checked the cervix 36 hours after my first +OPK and it had closed, so we knew we nailed the timing. Some people will ovulate earlier or later, so check all the signs to determine your timing.
We purchased a plastic speculum online, which came in sterile packaging. After positioning the speculum (it was more comfortable to do that part myself), DP used a sterile cotton swab to gently remove the cervical mucous from the os/cervix before inserting the sterile catheter of sperm. The catheter was inserted through the os just to the point of resistance. The sperm was slowly deposited, and the catheter slowly removed. I didn't feel a thing.
I stayed lying down for awhile (periodically turning to either side, just in case it'd help!). I did have some mild cramping after the first insem. If you notice anything worse than mild cramping, see a doctor - you could have punctured the uterus with the catheter, or the catheter may have pushed some foreign object/secretion/etc. from your vagina into the uterus - a uterine infection is very serious.
Fortunately for us, it only took this cycle to conceive our now 2-year old son.