It might be a little bit complicated, but Google already huge provided Docs about this usage. 
To request stored credentials, you must create an instance of GoogleApiClient configured to access the Credentials API.
mCredentialsApiClient = new GoogleApiClient.Builder(this)
    .addConnectionCallbacks(this)
    .enableAutoManage(this, this)
    .addApi(Auth.CREDENTIALS_API)
    .build();
A CredentialRequest object specifies the sign-in systems from which you want to request credentials. Build a CredentialRequest using the setPasswordLoginSupported method for password-based sign-in, and the setAccountTypes() method for federated sign-in services such as Google Sign-In.
mCredentialRequest = new CredentialRequest.Builder()
    .setPasswordLoginSupported(true)
    .setAccountTypes(IdentityProviders.GOOGLE, IdentityProviders.TWITTER)
    .build();
After you have created GoogleApiClient and CredentialRequest objects, pass them to the CredentialsApi.request() method to request credentials stored for your app.
Auth.CredentialsApi.request(mCredentialsClient, mCredentialRequest).setResultCallback(
    new ResultCallback<CredentialRequestResult>() {
        @Override
        public void onResult(CredentialRequestResult credentialRequestResult) {
            if (credentialRequestResult.getStatus().isSuccess()) {
                // See "Handle successful credential requests"
                onCredentialRetrieved(credentialRequestResult.getCredential());
            } else {
                // See "Handle unsuccessful and incomplete credential requests"
                resolveResult(credentialRequestResult.getStatus());
            }
        }
    });
On a successful credential request, use the resulting Credential object to complete the user's sign-in to your app. Use the getAccountType() method to determine the type of retrieved credentials, then complete the appropriate sign-in process. 
private void onCredentialRetrieved(Credential credential) {
    String accountType = credential.getAccountType();
    if (accountType == null) {
        // Sign the user in with information from the Credential.
        signInWithPassword(credential.getId(), credential.getPassword());
    } else if (accountType.equals(IdentityProviders.GOOGLE)) {
        // The user has previously signed in with Google Sign-In. Silently
        // sign in the user with the same ID.
        // See https://developers.google.com/identity/sign-in/android/
        GoogleSignInOptions gso =
                new GoogleSignInOptions.Builder(GoogleSignInOptions.DEFAULT_SIGN_IN)
                        .requestEmail()
                        .build();
        mGoogleApiClient = new GoogleApiClient.Builder(this)
                .enableAutoManage(this, this)
                .addApi(Auth.GOOGLE_SIGN_IN_API, gso)
                .setAccountName(credential.getId())
                .build();
        OptionalPendingResult<GoogleSignInResult> opr =
                Auth.GoogleSignInApi.silentSignIn(mGoogleApiClient);
        // ...
    }
}