You can add the following to the AndroidManifest.xml file inside the activity that has to open the file (pdf in our case)
<intent-filter >
<action android:name="android.intent.action.VIEW" />
<category android:name="android.intent.category.DEFAULT" />
<data android:mimeType="application/pdf" />
</intent-filter>
Make sure you specify the proper mime format. The user will be prompted to choose your app if she wants to open the “pdf” file.
Check also Android intent filter: associate app with file extension for more details.