Copy from http://software.intel.com/en-us/articles/connecting-to-google-drive-from-an-android-app?1

GoogleDriverSample

package com.intel.driveapp;

import android.os.Bundle;
import android.os.Environment;
import android.provider.MediaStore;
import android.app.Activity;
import android.view.Menu;
import android.view.View;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

import java.io.FileOutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import android.accounts.AccountManager;
import android.content.ContentResolver;
import android.content.Context;
import android.content.Intent;
import android.database.Cursor;
import android.net.Uri;
import android.widget.AdapterView;
import android.widget.AdapterView.OnItemClickListener;
import android.widget.ArrayAdapter;
import android.widget.Button;
import android.widget.ListView;
import android.widget.Toast;

import com.google.api.client.extensions.android.http.AndroidHttp;
import com.google.api.client.googleapis.extensions.android.gms.auth.GoogleAccountCredential;
import com.google.api.client.googleapis.extensions.android.gms.auth.UserRecoverableAuthIOException;
import com.google.api.client.http.FileContent;
import com.google.api.client.http.GenericUrl;
import com.google.api.client.json.gson.GsonFactory;
import com.google.api.services.drive.Drive;
import com.google.api.services.drive.DriveScopes;
import com.google.api.services.drive.model.File;


public class MainActivity extends Activity 
{
	static final int 				REQUEST_ACCOUNT_PICKER = 1;
	static final int 				REQUEST_AUTHORIZATION = 2;
	static final int 				RESULT_STORE_FILE = 4;
	private static Uri 				mFileUri;
	private static Drive 			mService;
	private GoogleAccountCredential mCredential;
	private Context 				mContext;
	private List<File> 				mResultList;
	private ListView 				mListView;
	private String[] 				mFileArray;
	private String 					mDLVal;
	private ArrayAdapter 			mAdapter;

	@Override
	protected void onCreate(Bundle savedInstanceState) 
	{
    	super.onCreate(savedInstanceState);

        // Connect to Google Drive
        mCredential = GoogleAccountCredential.usingOAuth2(this, Arrays.asList(DriveScopes.DRIVE));
        startActivityForResult(mCredential.newChooseAccountIntent(), REQUEST_ACCOUNT_PICKER);
        
        mContext = getApplicationContext();
		
		setContentView(R.layout.activity_main);
		mListView = (ListView) findViewById(R.id.listView1);
		
		OnItemClickListener mMessageClickedHandler = new OnItemClickListener() 
		{
		    public void onItemClick(AdapterView parent, View v, int position, long id) 
		    {
		    	downloadItemFromList(position);
		    }
		};

		mListView.setOnItemClickListener(mMessageClickedHandler); 
		
		final Button button = (Button) findViewById(R.id.button1);
        button.setOnClickListener(new View.OnClickListener() 
        {
            public void onClick(View v) 
            {
            	final Intent galleryIntent = new Intent(Intent.ACTION_PICK);
                galleryIntent.setType("*/*");
                startActivityForResult(galleryIntent, RESULT_STORE_FILE);
            }
        });
        
        final Button button2 = (Button) findViewById(R.id.button2);
        button2.setOnClickListener(new View.OnClickListener()
        {
            public void onClick(View v) 
            {
            	getDriveContents();
            }
        });
	}
	
	private void getDriveContents()
	{
		Thread t = new Thread(new Runnable() 
    	{
    		@Override
    		public void run() 
    		{
                mResultList = new ArrayList<File>();
				com.google.api.services.drive.Drive.Files f1 = mService.files();
				com.google.api.services.drive.Drive.Files.List request = null;
				
				do 
				{
					try 
					{ 
						request = f1.list();
						request.setQ("trashed=false");
						com.google.api.services.drive.model.FileList fileList = request.execute();
						
						mResultList.addAll(fileList.getItems());
						request.setPageToken(fileList.getNextPageToken());
					} catch (UserRecoverableAuthIOException e) {
						startActivityForResult(e.getIntent(), REQUEST_AUTHORIZATION);
					} catch (IOException e) {
						e.printStackTrace();
						if (request != null)
						{
							request.setPageToken(null);
						}
					}
				} while (request.getPageToken() !=null && request.getPageToken().length() > 0);
				
				populateListView();
    		}
    	});
    	t.start();
	}
	
	private void downloadItemFromList(int position)
	{
		mDLVal = (String) mListView.getItemAtPosition(position);
    	showToast("You just pressed: " + mDLVal);
    	
    	Thread t = new Thread(new Runnable() 
    	{
    		@Override
    		public void run() 
    		{
		    	for(File tmp : mResultList)
				{
					if (tmp.getTitle().equalsIgnoreCase(mDLVal))
					{
						if (tmp.getDownloadUrl() != null && tmp.getDownloadUrl().length() >0)
						{
							try
							{
								com.google.api.client.http.HttpResponse resp = 
										mService.getRequestFactory()
										.buildGetRequest(new GenericUrl(tmp.getDownloadUrl()))
										.execute();
								InputStream iStream = resp.getContent();
								try 
								{
									final java.io.File file = new java.io.File(Environment
											.getExternalStoragePublicDirectory(Environment.DIRECTORY_DOWNLOADS).getPath(), 
											tmp.getTitle());
									showToast("Downloading: " + tmp.getTitle() + " to " + Environment
											.getExternalStoragePublicDirectory(Environment.DIRECTORY_DOWNLOADS).getPath());
									storeFile(file, iStream);
								} finally {
									iStream.close();
								}
								
							} catch (IOException e) {
								e.printStackTrace();
							}
						}
					}
				}
    		}
    	});
    	t.start();
	}
	
	private void populateListView()
	{
		runOnUiThread(new Runnable() 
		{
			@Override
			public void run() 
			{
				mFileArray = new String[mResultList.size()];
				int i = 0;
				for(File tmp : mResultList)
				{
					mFileArray[i] = tmp.getTitle();
					i++;
				}
				mAdapter = new ArrayAdapter<String>(mContext, android.R.layout.simple_list_item_1, mFileArray);
				mListView.setAdapter(mAdapter);
			}
		});
	}
	
	private void storeFile(java.io.File file, InputStream iStream)
	{
		try 
		{
			final OutputStream oStream = new FileOutputStream(file);
			try
			{
				try
				{
					final byte[] buffer = new byte[1024];
					int read;
					while ((read = iStream.read(buffer)) != -1)
					{
						oStream.write(buffer, 0, read);
					}
					oStream.flush();
				} finally {
					oStream.close();
				}
			} catch (Exception e) {
				e.printStackTrace();
			}
		} catch (IOException e) {
			e.printStackTrace();
		}
	}

	@Override
	public boolean onCreateOptionsMenu(Menu menu) {
		getMenuInflater().inflate(R.menu.main, menu);
		return true;
	}
	
	@Override
    protected void onActivityResult(final int requestCode, final int resultCode, final Intent data) 
	{
		switch (requestCode) 
		{
			case REQUEST_ACCOUNT_PICKER:
				if (resultCode == RESULT_OK && data != null && data.getExtras() != null) 
				{
					String accountName = data.getStringExtra(AccountManager.KEY_ACCOUNT_NAME);
					if (accountName != null) {
						mCredential.setSelectedAccountName(accountName);
						mService = getDriveService(mCredential);
					}
				}
				break;
			case REQUEST_AUTHORIZATION:
				if (resultCode == Activity.RESULT_OK) {
					//account already picked
				} else {
					startActivityForResult(mCredential.newChooseAccountIntent(), REQUEST_ACCOUNT_PICKER);
				}
				break;
			case RESULT_STORE_FILE:
				mFileUri = data.getData();
				// Save the file to Google Drive
        		saveFileToDrive();
				break;
		}
	}
    
    private Drive getDriveService(GoogleAccountCredential credential) {
        return new Drive.Builder(AndroidHttp.newCompatibleTransport(), new GsonFactory(), credential)
            .build();
      }

    
    private void saveFileToDrive() 
    {
    	Thread t = new Thread(new Runnable() 
    	{
    		@Override
    		public void run() 
    		{
				try 
				{
					// Create URI from real path
					String path;
					path = getPathFromUri(mFileUri);
					mFileUri = Uri.fromFile(new java.io.File(path));
					
					ContentResolver cR = MainActivity.this.getContentResolver();
					
					// File's binary content
					java.io.File fileContent = new java.io.File(mFileUri.getPath());
					FileContent mediaContent = new FileContent(cR.getType(mFileUri), fileContent);

					showToast("Selected " + mFileUri.getPath() + "to upload");

					// File's meta data. 
					File body = new File();
					body.setTitle(fileContent.getName());
					body.setMimeType(cR.getType(mFileUri));

					com.google.api.services.drive.Drive.Files f1 = mService.files();
					com.google.api.services.drive.Drive.Files.Insert i1 = f1.insert(body, mediaContent);
					File file = i1.execute();
					
					if (file != null) 
					{
						showToast("Uploaded: " + file.getTitle());
					}
				} catch (UserRecoverableAuthIOException e) {
					startActivityForResult(e.getIntent(), REQUEST_AUTHORIZATION);
				} catch (IOException e) {
					e.printStackTrace();
					showToast("Transfer ERROR: " + e.toString());
				}
    		}
    	});
    	t.start();
	}

	public void showToast(final String toast) {
		runOnUiThread(new Runnable() {
			@Override
			public void run() {
				Toast.makeText(getApplicationContext(), toast, Toast.LENGTH_SHORT).show();
			}
		});
	}
	
	public String getPathFromUri(Uri uri) 
	{
        String[] projection = { MediaStore.Images.Media.DATA };
        Cursor cursor = getContentResolver().query(uri, projection, null, null, null);
        int column_index = cursor
                .getColumnIndexOrThrow(MediaStore.Images.Media.DATA);
        cursor.moveToFirst();
        return cursor.getString(column_index);
	}

}