I just got a new iMac 10.9. adobe flash keeps asking for my password. I don't have one. they set my iMac up for me at the computer place. Help!

If that's the real Adobe Flash Player, then it probably wants an update. If so, it's asking for your local administrative password; the password you use to log in.

As for Adobe Flash Player in general, the safest course is to download the Adobe product removal tool and remove Adobe Flash Player — Adobe Flash Player has a long history of issues, and it's been one of the more common paths for malware onto your Mac. Always go to the canonical distribution site for any of these tools — the Adobe web site, in this case — and the uninstaller is available here. Going to another location or to a download web site — even some of the better known download aggregator sites — can end up installing other software, and adware.

When you start the computer and the main screen comes up with user icons, do you enter a password to get in? Use it.

nork74 wrote:

I don't have a password. I just turn on my computer and go!

Yes, you do have a password. The folks that set up your Mac apparently just didn't tell you what it was. Here is one of the descriptions on how to reset the password to something you do know, though the folks that originally configured this might remember what password they used. (Worst case, it's a weak password and subject to hacking. Here is how to pick a secure password.)