How to open a website when a Button is clicked in Android application?

If you are talking about an RCP app, then what you need is the SWT link widget.

Here is the official link event handler snippet.

Update

Here is minimalist android application to connect to either superuser or stackoverflow with 2 buttons.

package ap.android;

import android.app.Activity;
import android.content.Intent;
import android.net.Uri;
import android.os.Bundle;
import android.view.View;

public class LinkButtons extends Activity {

    @Override
    public void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.main);
    }

    public void goToSo (View view) {
        goToUrl ( "http://stackoverflow.com/");
    }

    public void goToSu (View view) {
        goToUrl ( "http://superuser.com/");
    }

    private void goToUrl (String url) {
        Uri uriUrl = Uri.parse(url);
        Intent launchBrowser = new Intent(Intent.ACTION_VIEW, uriUrl);
        startActivity(launchBrowser);
    }

}

And here is the layout.

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android" android:orientation="vertical" android:layout_width="fill_parent" android:layout_height="fill_parent">
    <TextView android:layout_width="fill_parent" android:layout_height="wrap_content" android:text="@string/select" />
    <Button android:layout_height="wrap_content" android:clickable="true" android:autoLink="web" android:cursorVisible="true" android:layout_width="match_parent" android:id="@+id/button_so" android:text="StackOverflow" android:linksClickable="true" android:onClick="goToSo"></Button>
    <Button android:layout_height="wrap_content" android:layout_width="match_parent" android:text="SuperUser" android:autoLink="web" android:clickable="true" android:id="@+id/button_su" android:onClick="goToSu"></Button>
</LinearLayout>

In your Java file write the following piece of code...

ImageView Button = (ImageView)findViewById(R.id.yourButtonsId);

Button.setOnClickListener(new OnClickListener() {
    public void onClick(View v) {
        Intent intent = new Intent();
        intent.setAction(Intent.ACTION_VIEW);
        intent.addCategory(Intent.CATEGORY_BROWSABLE);
        intent.setData(Uri.parse("http://www.yourURL.com"));
        startActivity(intent);
    }
});

Here is a workable answer.

Manifest.xml

<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://schemas.android.com/apk/res/android"
  package="com.tutorial.todolist"
  android:versionCode="1"
  android:versionName="1.0">
  <uses-sdk android:minSdkVersion="3"></uses-sdk>
  <application android:icon="@drawable/icon" android:label="@string/app_name">
    <activity android:name=".todolist"
              android:label="@string/app_name">
        <intent-filter>
            <action android:name="android.intent.action.MAIN" />
            <category android:name="android.intent.category.LAUNCHER" />
        </intent-filter>
    </activity>
  </application>
</manifest>

todolist.java

package com.tutorial.todolist;
import android.app.Activity; 
import android.content.Intent;
import android.net.Uri;
import android.os.Bundle; 
import android.view.View;
import android.view.View.OnClickListener;
import android.widget.Button;

public class todolist extends Activity {    
    @Override
    public void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.main);

        Button btn = (Button) findViewById(R.id.btn_clickme);
        btn.setOnClickListener(new OnClickListener() {
            public void onClick(View v) {
                Intent myWebLink = new Intent(android.content.Intent.ACTION_VIEW);
                myWebLink.setData(Uri.parse("http://www.anddev.org"));
                    startActivity(myWebLink);
             }
        });
    }
}

main.xml

<?xml version="1.0" encoding="utf-8"?> 
<LinearLayout xmlns:android="schemas.android.com/apk/res/android"
  android:orientation="vertical" 
  android:layout_width="fill_parent" 
  android:layout_height="fill_parent" > 

    <Button android:id="@+id/btn_clickme" 
      android:text="Click me..." 
      android:layout_width="fill_parent" 
      android:layout_height="wrap_content" /> 
</LinearLayout>

Import import android.net.Uri;

Intent openURL = new Intent(android.content.Intent.ACTION_VIEW);
openURL.setData(Uri.parse("http://www.example.com"));
startActivity(openURL);

or it can be done using,

TextView textView = (TextView)findViewById(R.id.yourID);

textView.setOnClickListener(new OnClickListener() {
    public void onClick(View v) {
        Intent intent = new Intent();
        intent.setAction(Intent.ACTION_VIEW);
        intent.addCategory(Intent.CATEGORY_BROWSABLE);
        intent.setData(Uri.parse("http://www.typeyourURL.com"));
        startActivity(intent);
    } });