If you are using a LATCH system, make sure that you follow the car seat manual's instructions along with your car's manual instructions. Have both of them handy when installing the seat. As I have stated before, if you do not have one or both of the manuals, then you can typically find an electronic copy on the manufacturer's website. You will need your car's manual as well because different cars have different LATCH systems. On some, the top tether will go over the head rest, on others, it will go under the headrest... different things like that.
If you are using a seat belt, make sure you place it in the proper slots. Especially if you have a convertible car seat. There will be a slot for rear facing and a slot for forward facing. If they are mixed up during installation, then the seat will not function properly in the event of a crash, which could lead to serious injury or death. Consulting your car seat's manual will help avoid any confusion. Here is an example of how NOT to install it a car seat.
This is Markai Durham and her little girl (from 16 and Pregnant). During these car seat posts I'm doing, you will probably get to see lots of babies from 16 and Pregnant featured because I see tons and tons of car seat misuse from girls on that show :( This one is just terrible. There are about 352436 things wrong with this picture, but since we are focusing on installation in this post, the seat belt has NO business being across that baby's lap!
When installing a rear-facing seat, the seat should typically be at a 45 degree angle. Many car seats are adjustable or have adjustable bases to aid in achieving this angle. Also, a lot of newer car seats will have a line that says it should be parallel to the ground in order for the seat to be installed properly, or they will have a thing on them that, when the car seat is at the correct angle, a certain color will show. I know that both of my kids' current car seats (Safety First Alpha Elite) have the line, and both of their infant car seats (they were both Graco) had the color indicator. The color indicator can be seen in the picture below. It is the the circle on the side of the car seat.