The terminal at DEN has a very simple layout. It's a single large rectangular building with 6 levels, 1 being the lowest and 6 being the highest, with roads passing along the east and west sides on levels 4, 5, and 6. The building is almost perfectly symmetrical from east to west.
The domestic baggage claim carousels are on level 5, on the east and west sides of the building, near the exit doors to the roads. So "West Terminal" here simply means that your airline's baggage claim is likely to be one of the carousels on the west side. There are many elevators and escalators in this area, so simply take one of them and go up one level. You'll then be on level 6 West. Go straight out the exit doors and you're at the curb where your driver will meet you.
Each exit door has a three-digit number. The first digit indicates the level 1-6, and even numbers are on the west side, odd numbers on the east side, increasing from north to south. So you'll likely go through a door numbered something like 608. Tell this number to your driver and they will know where to find you. Or they might tell you to wait outside a specific door number.
In case they want to meet you on the east side instead (odd numbered doors), you would simply walk straight through the terminal from west to east and exit on the east side.
If you're arriving straight from an international origin point, then you will instead claim your luggage as you pass through customs. You exit customs at the north end of the terminal on level 5. So if you want to get to level 6 West, just keep right as you exit customs and take any elevator or escalator up one level, then exit to the road. (For East, keep left instead.)
The only thing about the DEN terminal that can be confusing is that because of its perfect symmetry, it can be easy to lose your orientation. Otherwise it's quite easy to navigate. It helps if you try to keep track of which way is North, or even bring a compass! (Your smart phone may have one built in; look for a corresponding app.)
By the way, if your destination is near central Denver, you should know that the airport is quite a ways from the city and a Lyft ride may be expensive. There is frequent train service from the airport into Denver (A Line), so you might consider taking the train to, say, Union Station in downtown Denver, and then taking Lyft from there. (Late evenings the train runs every 30 minutes.) The exit to the airport train station is at the south end of the terminal on level 5, and then you go down another long escalator. The fare is $9 and the train is relatively fast.
Enjoy your visit!