For me, it depended on what the acupuncture was for. When it was just general, not really focusing on anything, I only noticed that I felt worse if I wasn't able to go for a week or two. I noticed immediate relief for my back pain. I went to a naturopathic doctor, who has training in Chinese medicine and acupuncture. The only thing it has not helped in pain I have in one of my wrists. No one knows why it hurts, nothing shows up on xray, and it still bothers me.
For acupuncture, you lie on a table in a room by yourself. You have to uncover the places where the needles will be put. Usually arms, legs to knee, and feet. Then the doctor put rubbing alcohol on the places where the needles will go in, to clean the area. The needles don't go in very deep, but can be very painful in some places. Then the needles are tapped in. After they're all in, you relax in the room for a while, and the doctor comes in to check on you. When the session is over, the needles are removed and you can get dressed. Sometimes, if they went too deep, you might bleed a little, but its usually not very bad and stops fast.
Sometimes I feel better as soon as its over, but other times it takes several sessions to notice anything.
If you have any needles put in the bottom of your hands, you might want to have someone else drive you home, since that area is usually very sensitive. This happened to me once, though only one of my hands hurt.
Also, you don't have to lie down. Sometimes, being on my back made it too difficult to breathe, so I was able to sit up. I think the most important thing is that you're resting. Having the needles in can also make it painful to move your arm or leg, if you want to move for some reason.
I have gone back every week, or every other week, but the person doing the acupuncture will let you know when they want to see you again.
This is just my experience, and other people will have different experiences.