Sperm collected by manual ejaculation into a clean container is processed (washed) to remove the sperm from the semen (liquid) and this sperm is then resuspended in an inert buffered media that is safe to place within the uterine cavity.
Unwashed (whole) semen with sperm is (generally) not placed within the uterine cavity since the semen contains molecules called prostaglandins that may cause severe uterine contractions (cramps).
To perform the insemination, a speculum is placed into the vaginal vault, the cervix is centered so that the opening of the os is clearly seen, washed sperm within media is drawn up into a sterile catheter and syringe (the usual volume of media for insemination is 0.5 mL), the tip of the catheter is slightly bent to negotiate the (occasionally tortuous) course through the cervical canal, and the catheter is gently fed into the uterine cavity. Once inside the uterus, the sperm and media is slowly injected into the cavity.
Discomfort or cramping is (in my experience) rare with intrauterine insemination