installing firefox


new mac user for a week I down load firefox it mounts to desktop. open up hard drive and put all files in applications. I open firefox it remounts to desk top. I hit eject and get error it is in use and can not be ejected. I thought once i put in the hard drive it would not remount to desktop and run normally?
How do I fix this.
What you stated as doing:

01. You downloaded 'Firefox 1.0.5.dmg', or equivalent, to your 'Desktop' (the default setting of 'Safari').
02. You double-clicked on the '.dmg' file, causing a disk image, titled 'Firefox', to also appear on your 'Desktop'. Also, the disk image automatically opened presenting a single MacOS X application file, titled 'Firefox'.
03. You dragged the (disk image's) application file 'Firefox' to your boot drive's 'Applications' folder. Actually, you said 'files'. You only need to drag the single 'Firefox' file to the 'Applications' folder, and no other file(s).

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What you now need to do:
01. If you currently have 'Firefox' launched - quit it.
02. Click on the disk image (if one currently exists on your 'Desktop') and drag it to the 'Dock' based trash can. It will then disappear from the 'Desktop'.
03. You still have the '.dmg' file on the 'Desktop' (or maybe now in the 'Applications' folder). It is a good idea to save this - to a CD, DVD or other media; in case you need to reinstall 'Firefox'.
04. Once you have backed up the '.dmg' file, it too can be dragged to the 'Dock' based trash can. You will have to manually empty the trash via 'Finder's 'Finder, Empty Trash' (or 'Finder, Empty Trash...) menu item.
05. Locate 'Firefox', in your 'Applications' folder, and double click on it - to launch it.

A nice option:
You may want to drag the 'Firefox' application icon, from the 'Appllications' folder onto the 'Dock'. This way you can easily launch 'Firefox' by merely clicking on the 'Dock' based 'Firefox' icon.
If you dragged the Firefox disk to your applications folder, you probably just have an alias of Firefox in there from that Firefox disk. Open the Firefox disk and drag just the Firefox icon to your app folder. Before opening Firefox, eject (trash the Firefox disk on the desktop.