How would I explore maps in Overwatch?

What you are looking for is the Custom Game option in the Play menu. You can choose the map, the map rotation, the difficulty and amount of AI players, etc. This should allow you to play privately or with friends in order to increase your knowledge of maps and heroes.

http://overwatch.wikia.com/wiki/Custom_Game

Edit: As to how the youtubers and others fly around the map, they use the custom game menu, and when viewing the team lineups page, they right click on their name and swap teams to the Spectator team. Then they start the match. This video shows how it can be done at around the 10:00 mark:

I do it like this: select Custom Game, then add 1 Bot Zarya to each team (because Zarya's attack is weak and she has a shield so their fight will be 100% VERY TOUGH :)), and then I add myself to Spectators. In the settings of the game select 1-map mode. This is the way where you have most time to explore the map.