How can I easily connect my old iMac to the new one I just bought, saving all of the files to the new one?

Per your request, I will be more specific. Apple provides us with an app specifically designed to do such transfers, called Migration Assistant. It is very easy to use. The basic steps are the following. Start both computers up and begin the setup process on the new Mac. If you have already done that, then follow the instructions Migration Assistant gives you. You will be asked if you want to transfer data from your old computer. Say yes. Connect both computers with a USB cable. Do not use Wi-Fi for the transfer. It is too slow and your data is likely to be corrupted due to the volume of data to be transferred. In the process you will be presented with some options as to what to transfer. Click the appropriate boxes.

I suggest that you do not copy your preferences and settings since you have apparently already set up the new computer. You can either have Migration Assistant copy your files or copy them over manually. You can not selectively transfer files.

You can either have Migration Assistant copy your apps or you can elect to download and reinstall them. In either case, some of them may require that they be reregistered to work in the new computer. In some cases, apps may need to be upgraded to work. There may be a cost to upgrade some of them. Your old operating system will not be transferred. All files in the old computer will remain intact. You may either transfer your data from the old Mac or from a Time Machine back up if you have back ups an are familiar with using Time Machine.

The transfer may take up to an hour, more or less, depending on the volume of data to be transferred.

If you plan to get rid of the old Mac, the following link explains what to do to prepare it.

What to do before you sell, give away, or trade in your Mac - Apple Support

Enjoy your new Mac.

Best way is if you have a Time Machine backup on the old one & move that drive over to Migrate from.