Ancient gear golem is easiest summoned using geartown which allows you to summon ancient gear monsters with one less tribute, ergo, you only need one monster to tribute to summon ancient gear golem. Ancient gear golem cannot be special summoned which make things difficult. Cards such as spell gear and ultimate ancient gear golem can special summon ancient gear golem from the deck and hand, or graveyard, respectively, but they require much more cost.
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Ultimate Ancient Gear Golem requires "Ancient Gear Golem" and 2 "Ancient Gear" monsters. Toon Ancient Gear Golem is an 'Ancient Gear' monster so it can take the part of one of the two 'Ancient Gear' monsters needed for the fusion. Note however there is an important distinction between saying (for example) "Ancient Gear" and "Ancient Gear monster". The first means, and only means, the Lv2 effect monster called "Ancient Gear" while the other means any monster with "Ancient Gear" in the name. That means that when Ultimate Ancient Gear Golem asks for "Ancient Gear Golem" and not "Ancient Gear Golem monster", it means, and only means, the original non-toon card just called "Ancient Gear Golem". "Toon Ancient Gear Golem" does not count for that part. You can see this same issue with Dark Magician's support cards, which support Dark Magician only and not anything else such as Skilled Dark Magician.
cards that specifically state that they cannot be special summoned from the graveyard, like ancient gear golem, or the very limited card: Tyler the great warrior (only one in the world) also an elemental hero fusion
Lava Golem's own special summon effect can only special summon itself to the opponent's side of the field. Like other 'can only be special summoned by..' monsters, if you summon it correctly, and it is then destroyed, it can be brought back to the field by cards like Monster Reborn. In Lava Golem's case, it will be special summoned to your side of the field if you do this.
Unless stated otherwise (Plaguespreader Zombie for example) a monster's special summon is done from hand only. Lava Golem must be in your hand, for you to be able to special summon it using the listed text on the card.
In either of your own main phases, you can special summon lava golem. Rather than offering the cost from your own side of the field, Lava Golem says to use the opponent's monsters. So you send the opponent's two monsters to the graveyard and place Lava Golem on their side of the field. Either player can try to negate it, in which case it will be destroyed and go to your graveyard.