A sample cloudformation template

template.yml

AWSTemplateFormatVersion: "2010-09-09"
Description: "My API Gateway and Lambda function"

Resources:
  SampleApi:
    Type: "AWS::ApiGateway::RestApi"
    Properties:
      Name: Sample

  SampleApiMethod:
    Type: "AWS::ApiGateway::Method"
    Properties:
      AuthorizationType: "NONE"
      HttpMethod: "GET"
      Integration:
        IntegrationHttpMethod: "POST"
        Type: "AWS_PROXY"
        Uri: !Sub
          - "arn:aws:apigateway:${AWS::Region}:lambda:path/2015-03-31/functions/${lambdaArn}/invocations"
          - lambdaArn: !GetAtt "SampleLambda.Arn"
      ResourceId: !GetAtt "SampleApi.RootResourceId"
      RestApiId: !Ref "SampleApi"

  SampleApiDeployment:
    Type: "AWS::ApiGateway::Deployment"
    DependsOn: "SampleApiMethod"
    Properties:
      RestApiId: !Ref "SampleApi"
      StageName: test

  SampleLambda:
    Type: "AWS::Lambda::Function"
    Properties:
      Code:
        ZipFile: |
          def handler(event,context):
            return {
              'body': 'Hello, world!',
              'headers': {
                'Content-Type': 'text/plain'
              },
              'statusCode': 200
            }
      Handler: "index.handler"
      Role: !GetAtt "SampleLambdaRole.Arn"
      Runtime: python3.7

  LambdaApiGatewayInvoke:
    Type: "AWS::Lambda::Permission"
    Properties:
      Action: "lambda:InvokeFunction"
      FunctionName: !GetAtt "SampleLambda.Arn"
      Principal: "apigateway.amazonaws.com"
      SourceArn: !Sub "arn:aws:execute-api:${AWS::Region}:${AWS::AccountId}:${SampleApi}/*/GET/"

  SampleLambdaRole:
    Type: "AWS::IAM::Role"
    Properties:
      AssumeRolePolicyDocument:
        Version: "2012-10-17"
        Statement:
          - Action: ["sts:AssumeRole"]
            Effect: "Allow"
            Principal:
              Service: ["lambda.amazonaws.com"]
      Policies:
        - PolicyDocument:
            Version: "2012-10-17"
            Statement:
              - Action: ["cloudwatch:*", "logs:*"]
                Effect: "Allow"
                Resource: "*"
          PolicyName: "lambdaLogPolicy"

  SampleLambdaLogGroup:
    DependsOn: SampleLambda
    Type: "AWS::Logs::LogGroup"
    Properties:
      LogGroupName: !Sub "/aws/lambda/${SampleLambda}"