To use the API key, you'd first go into the Administration section of the Maximo-X work center (for Maximo 7.6.1.x) found at: [your Maximo URL here]/maximo-x/#/adminstrator/integration. There should be a tab for API keys where you can click the "Add API Key" button and then select a user and a token expiration length (-1 for permanent), then click Add. For any future requests then, all you need to do is include the API key as a URL parameter, which if I remember correctly is [your Maximo URL here]/[whatever your endpoint is]?apikey=[your API key goes here]
Keep in mind, with this approach, all activity from that application will now be under that specific user.
The other option would be to make a REST API request to the apikey endpoint first using the current user's supplied credentials. This will generate an API for that particular user and then just use that apikey for that user moving forward, but then you'd likely need to store that apikey locally which may or may not be secure depending on your application.
Hope that helps!