A while back, I posted my tried-and-proven aircraft forward-facing toddler seat installation technique. Unfortunately, the search function isn't turning up the post for some reason, so I'll post it again.
1) Shortest/smallest person will usually be best at installing a carseat on an airplane; bigger adults tend to hit their heads on the bottom of the overhead bin when they try to do it. Smaller hands tend to be easier, too.
2) If possible, get yourself and the seat on before most of the passengers board, especially if you are short. A carseat has to be carried down the aisle above the level of the seats; it will almost never fit in the aisle proper. If you're short, the best way to carry it is upside down and sideways over your arm; that way you can still see over the seat as you carry it. (Think of the profile of the number 7. That's the best way to carry it.) On some airlines that will not allow you to preboard the seat to install it, I have occasionally had luck w/ asking politely for one of the ramp agents to be allowed to just set it down in the proper row before boarding starts. They can't install it, but if you beg nicely, they may drop it onto seat 27A for you, especially if you are the only adult in the party.
3) To install the seat (in the window position, of course): first extend the aircraft seat's belt to the longest possible length, leaving just a couple of inches' tab so that you will be able to grab it to tighten it later in the process. Raise the armrests between the seats. Lean on the seatback and recline the seat as far as it will go. Put the carseat in position and thread the airline seat's belt through the slots, then buckle that belt. Put one knee into the seat of the carseat, then pull the tab of belt you left; the buckle of the aircraft seatbelt should slide down and disappear behind the carseat. Pull it tight, remove your knee, and then push the recline button and put the aircraft seatback upright again (you may have to pull the headrest toward you.) At this point, your carseat should be firmly fastened into the frame of the aircraft seat.
4) A properly-installed carseat may be hard to remove, b/c you may not be able to get your hand behind the carseat to undo the buckle. If this happens, wait until the passengers behind you have left, then go around to that row and reach up between the seatback and the seat cushion; it should be very easy to release the latch from that position.
One note: with an infant seat, it is likely that you will not be able to properly secure it using a separate base. Because aircraft belts latch in the center rather than at the side, there is a good possibility that the position of the buckle will prevent the seat from properly locking into the base. All infant seats sold in the US can be installed without the base using only a lap belt; check your instructions if you have been using the base and don't know how to install the seat without it.