In whichever panel you've created your presets, there's usually a Preset Manager. For example, if you click the icon in the upper left for your brush presets and then click the widget on the upper right of that panel, you'll see a listing for a Preset Manager in there. Once that's open, you can shift-click (for everything between the first and 2nd click), or ctrl/cmd click (for stuff that's distributed around the panel), and select Save Presets. The default location will come up. At that point, you should note that default location and access it through your OS to copy that file, or you can switch to someplace like your desktop to save the resultant file (if you do change the save location, Photoshop may continue to remember that location for any other preset saves you attempt). From there, you can move the file with keychain drive or something, and move it to your new computer. Once on that computer, you can then use the dialog box again to choose Load Presets, and navigate to your saved file.
If this doesn't clarify - or it's too convoluted, please note here, and I'll try to make a little video when I get back to my main computer.
It will help to know your PS version and which OS you're using.
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