The most important role for a brake lever is to be an efficient actuator for brakes. Aero levels tend to be more ergonomic for riding the hoods. The pivot is usually further up in the handle, making braking from the hoods more comfortable and easy. Aero levers seem to provide better braking from the hoods, at least, than old, non-aero ones.
Take the aero lever and slide it on. You may have to rotate it around and get it roughly into place. One thing to be aware of, the levers are marked left and right. If not, there are notches where the cables come out. So the notches should come to be towards the inside of the handlebars.
Get it roughly up where you want it to be, find the little bolt for the clamp and tighten it down.install the aero lever and cable
Use a straight edge. Line the straight edge up with the flat part of the bottom of the handlebar (taking a vintage bike for example) and let the bottom of the brake lever touch the straight edge. Then clamp the brake lever down.
Do the same on the other side.
Open the brake lever and insert the cable inside. There are a wide opening on one side if you rotate the little part in the brake lever and a narrow opening on the other side. Let the wide opening facing forward, insert the cable into the opening and push it out through the back.
Slide the cable into the housing. On a lot of aero breaks, you need a ferrule that goes on to the lever end of the cable housing. Adjust the length of the cable housing and give it a new and clean cut.
Insert the cable through the break and pull the cable down. Take the little barrel adjuster close all the way and then unscrew it about three or four full turns.
Close the brakes against the hub and pull the cable as tight as you can. Then tighten the screw on the adjuster. Cut the excess end. Do the same on the other side.install the aero lever and cable
Tape the cable to the handlebar with the cable inside of the curve of the handlebar. Aero levers have the cabling running under the hoods and under the bar tape, as opposed to old drop bar levers with the cables leaving the levers from the top/peak of the hood. The wrapped cables do make the bike look cleaner.
Check the brake.
Pulling more (millimeters) of cable would correspond to lower mechanical advantage in the lever body, and more travel at the brake shoe. When a brake lever pulls too little cable, the brakes feel super squishy and you have to run the brake pads super close to the rim. When a brake lever pulls too much cable, the brakes feel "pukka-pukka" but you don't get much power. An aero lever does pull a bit less cable length, for the motion of the brake lever.