Step 1: Connect your Android phone to computer.
You can refer to this step by step guide on how to connect android phone to computer.
Step 2: Run PC Tool for VeryAndroid SMS Backup on computer.
Click "PCToolforSMS.exe" on your computer to run direclty. Then click "Menu" -> "Backup SMS from Android".

Step 3: Backup successfuly.
All your SMS on Android phone are saved on your computer now.

Now you can manage your SMS on computer easily.

Free Download it to try.
Read more guides about it from: http://www.veryandroid.com/how-to-use-veryandroid-sms-backup.html