my late 2013 iMac running latest OS Catalina is very very slow. I also have a 2019 MacBook Air which is very very fast. please advise.

A 2103 iMac can very well run Catalina with pretty decent performance.

Two things may have a huge impact:

RAM - have at least 8GB

Drive - if this Mac has only a rotating hard drive, then this is probably what causes poor performance.

Get an external SSD connected via USB3 and you'll get a huge upgrade for a lot less than $100.

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You first have to have Catalina installed on the SSD, of course. You can do this either by downloading the installer from the App Store, or by cloning the internal HD to the SSD.

Once you have a bootable system on the SSD, you select it in the usual way: either you start your mac holding down the Option key - which presents you with a list of bootable drives to choose from - or you change the startup drive directly in System Preferences->Startup Disk.

Is there any special procedure for getting your iMac to use the external SSD instead of the internal HD?

I have a 2013 27" iMac also. My iMac would just turn off using Catalina. I went back High Sierra and my iMac appears to running OK but it has the original HD.