In Path of Exile, Mapping can be a controversial philosophy. The fact is, many players may not know how to start mapping, or how to run a map. Don't be panic, the following post will tell you some tips.
You should do something when you start mapping. You will find a few maps naturally while playing through Acts 8-10. You must have completed the final story boss, Act 10 Kitava to start mapping. Kitava is much harder than most early map bosses so feel confident to jump straight into maps.
You should not doing the Graveyard or Dungeon maps initially as the bosses are both very powerful. The best map for beginners is probably Beach as it has a relatively easy boss and is open and linear.
Once you have rolled the map you want to try, go to the map device in the Templar Laboratory or your Hideout and put in the map. Note the map device has four slots but for the majority of maps you will only need to use the one slot. After activating you will notice six portals appear. This represents how many times you can exit and re-enter the map. After using all six portals the map cannot be entered again. After entering the map you can start killing monsters.
Hopefully after clearing your first map you have found some more maps. Be aware that sometimes you will have a bad streak of maps where no other maps drop. This is expected as other times a single map instance will drop lots of maps. The aim of mapping is to find maps of higher level tiers.
Generally, you should run any maps that can potentially drop new maps in your Atlas. Always aim to get the map completion bonus when running a map for the first time. Completing the Atlas as much as possible is definitely the best way to go for the majority of players. More experienced players may want to look at different strategies you can use to optimize your Atlas for gaining poe orbs or experience.
Some people argue you should always run your highest tier map, other people say you should build a strong base on each tier before progressing to the next tier. There is no right or wrong answer. Running any maps that does not give you diminishing experience.