Let's say you have a Lambda Function, perhaps something like this (Python in this example). In this example, the print(event) statement will append logs to Cloudwatch.

import json

def lambda_handler(event, context):

    print(event)

    return {
        'statusCode': 200,
        'body': json.dumps({
            "greeting":"hello",
            "foo": event['queryStringParameters']['foo']
        })
    }

An API Gateway HTTP API with a route, such as a GET route or POST route, can be used so that a GET or POST request can be made to your Lambda Function over HTTP.

The aws apigatewayv2 get-apis command can be used to list the API Gateway HTTP APIs you have created.

~]$ aws apigatewayv2 get-apis
{
    "Items": [
        {
            "Name": "foo",
            "Tags": {},
            "ProtocolType": "HTTP",
            "RouteSelectionExpression": "$request.method $request.path",
            "ApiId": "abcdefg123",
            "ApiEndpoint": "https://abcdefg123.execute-api.us-east-1.amazonaws.com",
            "ApiKeySelectionExpression": "$request.header.x-api-key",
            "CreatedDate": "2023-12-06T02:12:32Z",
            "DisableExecuteApiEndpoint": false
        }
    ]
}

And here is how you could GET using curl with data.

~]$ curl --request GET --url https://abcdefg123.execute-api.us-east-1.amazonaws.com/myEndpoint?foo=bar
{"greeting": "hello", "foo": "bar"}

Then, in Cloudwatch > Log groups > /aws/lambda/myapi > yyyy/mm/dd/[$LATEST]abcdefg123456789abdefg123456789, you should have something like this.

{
   "version":"2.0",
   "routeKey":"GET /myendpoint",
   "rawPath":"/myendpoint",
   "rawQueryString":"foo=bar",
   "headers":{
      "accept":"*/*",
      "content-length":"0",
      "host":"abcdefg.execute-api.us-east-1.amazonaws.com",
      "user-agent":"curl/8.0.1",
      "x-amzn-trace-id":"Root=1-656fe245-0f4b84cd29eb21af126bd7c8",
      "x-forwarded-for":"10.11.12.13",
      "x-forwarded-port":"443",
      "x-forwarded-proto":"https"
   },
   "queryStringParameters":{
      "foo":"bar"
   },
   "requestContext":{
      "accountId":"123456789012",
      "apiId":"cl88zvqi38",
      "domainName":"abcdefg.execute-api.us-east-1.amazonaws.com",
      "domainPrefix":"abcdefg",
      "http":{
         "method":"GET",
         "path":"/myendpoint",
         "protocol":"HTTP/1.1",
         "sourceIp":"10.11.12.13",
         "userAgent":"curl/8.0.1"
      },
      "requestId":"PgBK5jaDIAMEJsQ=",
      "routeKey":"GET /myendpoint",
      "stage":"$default",
      "time":"06/Dec/2023:02:53:57 +0000",
      "timeEpoch":1701831237455
   },
   "isBase64Encoded":false
}

You may also want to create a Cloudwatch Alarm so that you are notified when your Lambda Function returns an error. Check out my article Create Lambda Function Cloudwatch Alarm using the AWS CLI.