There are a few ways you can change your game mode.
The first involves enabling cheats before you create your world (singleplayer). After you create your world, press t. This should bring up a chat at the bottom. Type /gamemode but don't press enter quite yet! The next thing is to decide what game mode you want. You can change from 3 game modes, survival, creative, and adventure. Let's say you want creative. Type /gamemode creative and you should be in creative.
Let's say you're in multiplayer (assuming your an op). You type /gamemode creative - but you want somebody else to have creative, a member that is not an op! Simply type their name after (or press tab after typing a couple letters of their name). /gamemode creative Notch if you wanted Notch to be in creative.
Lastly, you can select the gamemode to creative before you create a world in singleplayer.
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If you install a mod it will work in all gamemodes.
With Minecraft premium you can use custom skins, play the full version of minecraft, which includes many new blocks, gamemodes, features and offline mode. In addition, you will be supporting Mojang so they can continue to make bigger and better updates.
There is no button to spawn eggs in minecraft, unless you are in creative mode in which case you press the Inventory button. Creative mode can be made to happen when you create a creative world or install a mod that lets you switch gamemodes ingame.
Unfortunately, you can not change your name on Minecraft!
You can change your minecraft clothes if you change your skin or download a mod.