Where is the gear icon?

"Restore" means to copy things from your backups to their original location.

You shouldn't have to delete things from your backups -- Time Machine will do that automatically, when the drive gets full. See Time Machine - Frequently Asked Question #12. But if you really want to delete things, that will show you how.

gwacfp wrote:

Thank you so much. I think I learned that. Also figured out there is no "gear icon" anymore,

Yes, there is, but it isn't in the default set of toolbar icons. From a Finder menubar, select Finder > View > Customize Toolbar and you can add it if you want.

However, despite statements to contrary, my TM does not delete old back-ups, and I cannot find any setting to make it do so. Every backup since I purchased my MacBook Air in June-July 2011 is still there, which is what is clogging up my system and created this need to delete them. If it deletes automatically I can't find where is the setting to have it do so.

There is no setting, as it's automatic.

It deletes "expired" backups on every backup: any backup over 24 hours old, except the first of the day, which is kept for a month. After a month, those are reduced to one per week for as long as there's room.

It only deletes old backups when it runs out of space.

It sounds like you have other data on your Time Machine drive. That's not a good idea; see Time Machine - Frequently Asked Question #3 for an explanation.

gwacfp wrote:

. . .

When I started with it I really had no idea what I was doing, I am very new to Macs

Apple does mention that in the Help, but it's not obvious -- rather hard to find, even if you know it's there!

--got one when I retired after iPhone and iPad. And moving the iTunes was such an ordeal I am reluctant to have to do it again, so not sure what to do now.

Your best bet is to simply get another HD, and use it exclusively for backups. Plus, have it also back up the other drive. See Time Machine - Frequently Asked Question #32 for details.

I want to download Mountail Lion. It won't let me, saying it needs 2gb of space and I don't have enough. Yet the system says I have 65 gb free.

Those are two different things. It needs a minimum of 2 GB of memory (RAM), and a minimum of 8 GB of free disk space.

Assuming your Mac is otherwise eligible (see http://www.apple.com/osx/specs/), you can add RAM yourself, or have an Apple Store or Apple Authorized Service Provider do it (that's more expensive, of course).

If you're going to do that, and your Mac will take more than 2 GB, put more on it. Mountain Lion will run with 2 GB, but if you're doing a lot of things at once, or photo or video editing, it may be rather slow.

The little booklet that came with your Mac should show how.

If you're not sure what model you have, or how much memory it can hold, type your Mac's serial number into this page: http://support.apple.com/specs/

(If you don't have the serial number handy, click the Apple logo at the left of your menubar and select About This Mac. On the next window, click where it shows the Version; that will show the Build number; click again and it will show the Serial Number.)

Click the link that will bring up. There's all sorts of info there; scroll down to the Processor and Memory section.

gwacfp wrote:

Hi,

After doing some checking, the Apple discussion site says my model [Macbook Air, late 2010] came with 2 gb of RAM

Then your Mac should be able to run Mountain Lion. If you're getting a message that it doesn't have enough RAM, there may be a problem with it. Try running this: OS X Lion: Use Apple Hardware Test Run the Extended tests (that may take half an hour or more). Write down any error code(s) it shows.

and more can't be added; whatever is there is fused/soldered into the motherboard or similar. Apparently I should have divined the need for more RAM when I purchased it, but I didn't. So am I just screwed?

No, you're not screwed. Mountain Lion will run on your Mac. It just may not be as fast as you'd like.