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There are a few resources I would suggest looking into if you want to do a client-side integration with LWC.
First off, the developer guide itself talks about options as far as making callouts directly from LWC, or via an Apex [proxy]2. The key things here are if you want to do a direct-from-client integration, you need to be certain to enable the CSP trusted site endpoint. And if you integrate via an Apex proxy, you must use a named credential in your HTTP request.
It sounds like you're looking at using the direct-from-LWC option.
Once you're familiar with the docs, I'd recommend taking a look at the dream-invest sample project which shows a basic API callout integration component and util module using an API key for authorization.
Once you get a basic callout working, of course feel free to come back with specific questions if you run into difficulties. There can be a number of hiccups you might encounter like with CORS, or more rigorous authorization settings required with certain APIs.