You are standing at the water heater with the cold supply line open in front of you. The expansion tank is still in its box. The job is to get it on the line, charged to the right pressure, and tested before the system fills and the wall goes back up.
Read the ratings first
Find the maximum working pressure on the water heater label. Then find the rating printed on the tank. The tank rating has to cover the heater rating. If it does not clearly cover it, stop and ask the installer or the local permitting office before you go further. Write both ratings on your clipboard.
Measure the house pressure
Thread a gauge onto a hose bib with nothing else running in the house. Read the static pressure, then write it down. The tank's air charge is set to match that figure, not the heater's rating. If the reading is high, a pressure-reducing valve is usually part of the picture. Ask who is responsible for that valve before you assume the tank alone will solve it.
Set the air charge before it touches water
The tank should be empty of water when you do this. Use a tire-type gauge on the air valve and bring the charge to the house reading. Give the gauge a few minutes to settle, then check again, because a reading can drift. Many tanks ship pre-charged, but check it anyway. A tank that arrives low will not hold its job.
Mount it on the cold side
The tank goes on the cold supply, upstream of the heater, through a tee or fitting the tank maker allows. Follow the orientation printed on the tank. Leave room to reach the air valve cap later. Support the tank with its bracket or a strap so the supply pipe does not carry its weight. Keep the connection clear of heat from the heater itself. Use fittings and joint methods your local code approves. If the work touches the potable line, a licensed plumber should do it or sign off on it.
Test before you close the wall
Open the supply and let the system fill fully. Open a hot tap and let the water run until it is steady. Look at the tank body and every joint for weeping or drips. Then check the air valve again after the system has run and settled. The charge should hold close to what you set. If it has dropped a lot, look for a leak at the valve or a fitting before you accept the install.
Write the install on the file
Record the house pressure reading, the charge you set, the tank rating, the tank location, and the install year. Note who did the work and whether a permit was closed. That file is what the next person will need when they plan the next service.
Questions to ask the installer
Ask what house pressure they measured and what charge they set. Ask for the tank rating in writing. Ask which fittings they used and whether the work was inspected. Ask whether the pressure-reducing valve was checked. Ask what the tank maker's documentation requires for the warranty to stay intact. The answers should be on paper, not only spoken.
If the system you have is a boiler rather than a tank heater, the boiler page on this site covers typical service life and when to plan a replacement.