The first 2-3 weeks are a training period. You are stretching parts which haven't been stretched for some time, and it's uncomfortable or even painful. You should do it for about 10 mins per day, just pumping up slowly, one hand pump at a time, and wait for the penis to draw in more blood and expand. When you get to the limit of what's comfortable, hold for about 5-10 seconds, and then let it fully down again. Repeat this for about 10 mins. You don't use any rings during the training period. If you ever get a bleed, release the vacuum immediately, pinch the location of the penis which is bleeding to stop it, and skip using the pump for a couple of weeks. It can happen if you try to pump up too fast without allowing the blood to catch up. They won't usually supply pumps to anyone on blood thinners beyond low dose asprin.
By 2-3 weeks, you will probably have found it's not painful any more. For penile rehab, you basically keep doing the same, but you can probably hold it pumped up for longer each time. Again, no rings are used. I was told to do it for 10 mins per day or 15 mins every other day.
If you want to use the pump for sex, then you have to learn how to use the rings. Don't put a ring on until you know how to get it off! As a test run one day, pump up and maintain the vacuum for 10-15 mins to make sure your OK with doing this. We were only taught how to use the Surefit silicone rings. When new, stretch it several times first like when you blow up a balloon. Stretch it over the end of the pump cylinder - don't use the loading cone (that's for the plastic rings - it will cause the silicone rings to fail faster). Then generate an erection. When you have an erection, slide the ring off the cylinder onto the base of the penis, being very careful not to catch a testicle in the ring. You should be able to release the vacuum, take the pump away, and maintain the erection. You can still use the pump while you have the ring on to top it up if necessary. If it goes down too fast to be useful, you should use a smaller ring or two rings by repeating the procedure and adding another ring. The pump only comes with a Medium (Y size) ring, but a pack of 3 containing small, medium, and large (X, Y, Z) is available on prescription in theory, and once you know which size ring, you can intercept the prescription and ask for the pharmacy to order 3 all the same size by adding a note to the order (there's no part number for 3 all the same size).
To take a ring off, grab the tabs and pull the ring open enough to get 2 or 4 fingers in too, and then stretch it to allow the blood to drain out of the penis. When erection has gone, keep it stretched and take it off. Don't try to take a ring off an erect penis - you'll likely do your penis some damage. Panicing and trying to rip it off an erect penis can be a disaster. Don't keep a ring on for more than 30 mins, and never allow yourself to fall asleep with one on - this will permanently damage the penis.
Men who attend a pump clinic and have the pump demoed on them are twice as likely to use it successfully afterwards. If you haven't had such a session, ask if your local hospital runs them. They're an off-shoot of the ED clinic, but shouldn't have much of a waiting list as they're usually run by the pump company reps rather than by clinicians.