Power drill (masonry bit required for brick or concrete)
Goggles, Mask as appropriate
Scout out your area! Find the optimal place to fasten the rings, which will be spaced 50 cm apart. Some enjoy in front of the TV, others near their computer or bed room. You will need enough space to perform ring push ups, so a little less than your height in front of the rings with space behind the rings for your chest and head. Be a little generous with your spatial calculations! You will also need room on either side of the rings for ring flyes, archer ring push ups, and attempts at the iron cross, so calculate that as a little less than your wing span. If you are crunched on space on either side don't worry, the exercises have workarounds!
Use a stud finder to ensure there are no wires, pipes, or anything else which will prohibit drilling. Judge the material in your ceiling. There is a good chance that even if it appears to be concrete, it may have a plaster coating with either wood or concrete behind it. Mark the ceiling with a pencil when you have found your optimal spots.
Don your goggles and mask, then use a power drill with a thin masonry tip (significantly smaller than your screws or bolts) to be extra sure your chosen spots are fine. If your ceiling fastener needs multiple screws/bolts, be sure to check all drill spots. Reminder: The rings need to be anchored 50 cm apart! You will know if you manage to drill through the material, so make sure the thickness is greater than your bolts or screws.
If you are mounting on wood, you may be ready to put in the screws. If you have difficulty putting the screws in, try using a larger bit, but still significantly smaller than the screw! Once the screws are in, hook your carabiner in and slide your ring straps through and you are done! Test your handiwork using your entire weight. Otherwise, switch to a larger drill bit, though slightly smaller than your concrete anchor and widen the holes. Put in the concrete anchor and tap gently with your hammer, slowly pushing it in. The anchor activates by twisting it, expanding the shield contraption. Twist until it can't possibly twist any more, then find something to use as leverage (say a wrench) and tighten it more. Hopefully, unless you are using eye bolts, you didn't forget to put up the fastener first because the bolt isn't coming out! Hook your carabiner in and slide the ring straps through and you are done! Except for the concrete dust everywhere from the drilling, get that stuff cleaned up ASAP.
Last words of advice:
Ensure that you have the appropriate screws or bolts than can individually support your weight, and then some. When pulling down on the rings, you are exerting force greater than your weight, especially if there is a sudden drop or swinging action. Rings are not a toy and should be treated with the utmost caution. Be sure to consider others who may share your space and be tempted to misuse the apparatus. Take down is simple with the carabiners, just unclip them. Attempt exercise moves cautiously if you are new to rings and assess your stability skills before trying new or advanced moves. When adjusting ring height, give a little tug to ensure you adjusted correctly.