The goal of the game is to break all of the other team's monuments (obsidian blocks and others, look for blocks with particle beams above them before game) and protect own. The team that has no monuments left loses. Last team that has any monuments wins.
Defence: When playing defensively, there are 2 approaches. The first is to try to mine all the blocks around the monument, so it is floating in air. This forces the other team to bridge to your monument, which can make them easy targets with your bow. The other approach is to build protecting walls and roofs around the monument. You can use items such as buttons and trapdoors to prevent the other team from placing blocks. Most importantly, remember about rushing. You cannot win without it.
Rush: There are several rush strategies, but we will try to cover the basic theory behind rushing on MonumentRush. First of all: Attack with a buddy! This make it significantly easier to attack, as one person can distract the defence while the other person breaks the monument. The person distracting doesn't have to even live, just give the other person enough time to break the monument. One trick you can use is to bridge way up in the sky (known as SkyBridging) and dropping down on their monument. You can avoid fall damage by crafting a boat and falling inside of it, as you don't take fall damage inside a boat.