The absolute best way to get around the city is by using the metro. CUA is very lucky to have its own Metro station and it is a lifesaver.
For first time users, here are is how to set up a Metro card:
Remember: GLENMONT GO HOME
This will save your life. When in doubt, instead of running over to a metro map or scrolling through your camera roll to find the map you saved, just remember that Glenmont takes you home to CUA. (Disclaimer: Glenmont go home works for most stops but if you are past the Brookland-CUA stop then you will need to go in the direction of Shady Grove.
Another way to get around the city is by using Uber. If you are a first time user, here is a $15 credit for a free ride. It will not always be free depending on how far you plan on going, though. Always make sure to check the price before accepting the Uber ride because if you walk a block or two you can lower the price.
If you just want to see the monuments at a quicker pace, and at a cheap price, then you can use the Capital Bike share. It is only $2 for 30 min. and $8 for 24 hours.