Let's hope your flights arrive/depart on time. You're arriving at terminal 2 on UA, so you simply walk out the front door, cross the first set of traffic and stay in the median/island. Look for the sign for rental cars and/or the light green buses (inter-terminal busses are darker green and will say "Gecko", "Roadrunner", or some other desert animal). Trip from T2 to car rental is ten minutes or less, plus however long it takes you to get the car. Drive back to the airport should be about five minutes.

From this point, you need to choose where you want to park - you can park in the T2 upper lot for a maximum of $8, but you'll have to walk or take the inter-terminal shuttle buses to T4, or you can park in the T4 parking (most convenient and most expensive, at something like $24 per day, not sure of the hourly rate). If the money doesn't mean much, park in T4 and enjoy the convenience. If the almost $20 you might save would be worth a decent dinner or something, park in T2 and cross back over to the median you waited for the bus earlier in the day - this time take the dark green inter-terminal bus to T4 (second stop). The shuttle ride is less than 5 minutes, but you might wait up to ten minutes for a bus to appear.

If you go for T2 parking, you'll want to stay in the right-hand lanes as you enter PHX. If you opt for T4, stay in the left-hand lanes, but prepare to merge right as you pass T3 (you'll need to go up a ramp for T4 in-terminal parking).

Ticketing is on level 2. If you take the inter-terminal bus, you arrive on level 1 and will need to take an elevator up. You should be able to use the US First/*G check-in lines (or use a kiosk if the lines are long and you're short on time). Once you check-in, you can probably use the fast-track security lines with your UA *G status. Not sure where you're flying to, but most western states departures happen out of the A gates, so you'll likely use the A-gate security checkpoint (I want to say it's "D", but I'm probably wrong).

Final note - if you're cutting it close on time and the lines for check-in are bad, consider going up to the gate level (level 3) to check-in - there are kiosks immediately before the security checkpoint for the A gates that are almost always free.

Have a safe and enjoyable trip!

Sean