How to open Gmail Compose when a button is clicked in Android App?

try {    
    Intent intent = new Intent (Intent.ACTION_VIEW , Uri.parse("mailto:" + "your_email"));
    intent.putExtra(Intent.EXTRA_SUBJECT, "your_subject");
    intent.putExtra(Intent.EXTRA_TEXT, "your_text");
    startActivity(intent);
} catch (ActivityNotFoundException e){
    //TODO smth
}

As JeffC pointed out, it is easy to essentially tell Android that you want to send something email-like and have Android give users a list of choices, which will probably include GMail. If you specifically want GMail, you have to be a bit cleverer. (Note that the correct MIME type is actually "text/plain", not "plain/text". Do to an implementation oddity, GMail seems to be the only activity which responds to the latter, but this isn't a behavior I would count on.)

The following App demonstrates the principle you can follow: actually examine all of the activities which say they can handle your SEND intent and see if any of them look like GMail.

package com.stackoverflow.beekeeper;

import android.app.Activity;
import android.content.Intent;
import android.content.pm.PackageManager;
import android.content.pm.ResolveInfo;
import android.os.Bundle;

import java.util.List;

public class StackOverflowTest extends Activity {
    /** Called when the activity is first created. */
    @Override
    public void onCreate(final Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.main);
        final Intent intent = new Intent(android.content.Intent.ACTION_SEND);
        intent.setType("text/plain");
        final PackageManager pm = getPackageManager();
        final List<ResolveInfo> matches = pm.queryIntentActivities(intent, 0);
        ResolveInfo best = null;
        for (final ResolveInfo info : matches)
           if (info.activityInfo.packageName.endsWith(".gm") ||
        info.activityInfo.name.toLowerCase().contains("gmail")) best = info;
        if (best != null)
           intent.setClassName(best.activityInfo.packageName, best.activityInfo.name);
        startActivity(intent);
    }
 }