This should teach you how to join multiplayer games either by yourself or with friends.
Solo Queue (1 player)
To begin, start at the home screen and click the large yellow button in the top of the screen. You should then be brought to the screen on the right. From this screen, you should see three buttons near the bottom of the screen, and additional buttons on the right of the screen. The button on the right are to choose your gamemode. However, for the time being most gamemodes are disabled besides the first gamemode.
Here is the translation and explanation of the game modes.
Eternal Arena: The classic DOTA/MOBA/LOL styled battle, but with 7v7 instead of 5v5.
Eternal Battlefield: Similar to the first mode, except with some differences. There is no shops and gold, you buy your build of items from the game store using your no pay gold or real cash. You can join at any point of a game in progress, and you can use all the champions for free, they are at level 18 by default. All the benefits you receive from Summoner Spells are doubled. Towers' are also all positioned in jungle instead of lanes.
Protect Athena: Athena is a champion in the game, in this mode, your mission is to use your chosen champion and protect her from many waves of monster attacks. Based on a chinese Warcraft 3 map of the same name. (Currently not yet available)
Zombie Invasion: As the name suggests, you are going to kill as many zombies as possible before your champion gets killed. (Currently not yet available)
DragonQuest: No, you are not going through dungeons, but there will be monsters in this mode. It still uses the traditional 3 lane map, however, the map is empty. You need to use summon stones to summon monsters, the higher level of the summon stone, the harder the monster. In order to obtain summon stones, you need to pay real money. After killing the monsters you had summoned, they will drop items and gemstones that you can use in Eternal Battlefield.
The buttons near the bottom of the screen are used to join a queue for games. In order to join a game by yourself, you need to press the left-most button. When you do this, you should be returned to the home page, with a small window in the top right corner. It should look something like this . That small window will tell you how many people are waiting to be matched with a game.(9 in the picture's case) Eventually, the game will match you with 6 teammates and 7 other players, and champion selection will begin.
Group Play (2+ players)
Again, starting from the home screen, click on the large red button in the top right hand corner. However, instead of choosing the left-most button, choose the button in the middle. This should bring you to the screen on the right. This is the Party menu, and allows you to invite friends to your group so you can all join the same game.
In order to invite friends to your group, click on the large green button. This should open up a second menu with a list of your friends and a small arrow next to their name. When you click on this arrow, their name should move over to the second column of this menu. This means you have added them to the invite list. Click the green button in this new menu in order to invite your selected friends. If you need help on adding friends, click on this link .