Mame now comes as a 7Zip self extracting archive. You can download it from the Mame development site here. There are two versions for either 32 or 64 bit systems. If you don't know which one to choose then have a look at the Mame Versions page.
Click the link for the version that you want and the file will download. Once downloaded, double-click the self exctracting file and a small window (shown below) will open. Just change the path to where you want Mame to extract to.
Most of the guides on EasyEmu will assume that you've extracted Mame to
The file will now extract Mame into the folder you've selected. The extracted folder structure and support files are explained on the Folders and Files page.