This is an old question, but it has no chosen answer, and I just solved this problem myself. Here's my solution:
Make sure you are set up to work with your Google API in the first place. See Google's list of prerequisites. I was working with Google My Business, so I also went through it's Get Started process.
In the OAuth 2.0 playground, Step 1 requires you to select which API you want to authenticate. Select or input as applicable for your case (in my case for Google My Business, I had to input https://www.googleapis.com/auth/plus.business.manage into the "Input your own scopes" input field). Note: this is the same as what's described in step 6 of the "Make a simple HTTP request" section of the Get Started guide.
Assuming successful authentication, you should get an "Access token" returned in the "Step 1's result" step in the OAuth playground. Copy this token to your clipboard.
Open Postman and open whichever collection you want as necessary.
In Postman, make sure "GET" is selected as the request type, and click on the "Authorization" tab below the request type drop-down.
In the Authorization "TYPE" dropdown menu, select "Bearer Token"
Paste your previously copied "Access Token" which you copied from the OAuth playground into the "Token" field which displays in Postman.
Almost there! To test if things work, put https://mybusiness.googleapis.com/v4/accounts/ into the main URL input bar in Postman and click the send button. You should get a JSON list of accounts back in the response that looks something like the following:
{
"accounts": [
{
"name": "accounts/REDACTED",
"accountName": "REDACTED",
"type": "PERSONAL",
"state": {
"status": "UNVERIFIED"
}
},
{
"name": "accounts/REDACTED",
"accountName": "REDACTED",
"type": "LOCATION_GROUP",
"role": "OWNER",
"state": {
"status": "UNVERIFIED"
},
"permissionLevel": "OWNER_LEVEL"
}
]
}