A Summon is the action of placing a Monster onto a Monster Zone. You can Summon a Monster either manually or with a Card Effect.
You always Summon Monsters face-up, unless you Special Summon with an Effect like "Morphing Jar 2", which states that the Monster is Special Summoned face-down.
You choose the Monster Zone
If you conduct a Summon, regardless the method, you will be the one who chooses which appropriate Monster Zone the Monster will be placed in (unless specified otherwise).
There are 10 different types of Summons:
A Tribute Summon is a Normal Summon which requires a Tribute. Fusion, Ritual, Synchro, XYZ, Pendulum, and Link Summons are all Special Summons.