Masterquest is quite simple.
You're on a fighter based on the screenshots above which is a feeder (base) class. The level for MQ on that class is 71. When you reach 71, you'll see a new building in town for doing the MQ. You click on it and confirm you'd like to do your MQ and it will automatically bring you up the steps. On the base feeder class there's 2 keys to pick from. You simply drag and drop a key onto the door and it will either explode or open. If it explodes you go back to lvl 1 and can try again on any feeder class. If it opens you go to the next door up the steps and put in the 2nd key. You will go back to lvl 1, but this time the next class will be available in character select (the samurai)
Feeder (Rogue, Fighter, Barbarian, Mage and Guardian) - lvl 71 to MQ and has 2 keys to unlock.
Samurai - lvl 73 to MQ and has 3 keys to unlock.
Paladin - lvl 75 to MQ and has 3 keys to unlock.
Monk - lvl 77 to MQ and has 4 keys to unlock.
Ninja - lvl 79 to MQ and has 4 keys to unlock.
Warlock - lvl 81 to MQ and has 5 keys to unlock.
Headhunter - lvl 83 to MQ and has 5 keys to unlock.
Alchemist - lvl 85 to MQ and has 6 keys to unlock.
Passing on Alchemist will reset the ladder where everyone goes back to lvl 1 on the feeder classes and a new season begins.
Feel free to ask any other questions and look here for plenty of info.
https://ladderslasher.d2jsp.org/index.php?g=4