It is not so difficult to backup iPhone 3gs to new iPhone 4. And you can see the steps below:
1.Make sure you have the latest version of iTunes, which is currently iTunes 10.5. You can download the latest version of iTunes from this link. Please install it after you download it.
2.Connect your current iPhone to iTunes and sync it. Verify that your original iPhone is backed up. For more information on how to do this, see iPhone about backups.
3.Connect your new iPhone to iTunes (on the same computer you used to back up your current iPhone).
4.iTunes will ask you if you want to restore from a backup or set up your new iPhone as a new phone.

If you have back up your text messages, you can restore from the backup.
To restore information from a backup, use one of the following methods after connecting your iOS device to the computer with which you normally sync:
1. Right-click (or Control-click) the device and choose Restore from Backup
2. If you have a new phone, you can connect to iTunes and it will prompt to restore from your backup

If you have no backup for your data on iPhone, iPhone data recovery software is your last shot! It's easy to use. Just a few clicks you can get all your data back.

Recently iCloud is a good choice to share data between i-device.

Yep, I can confirm that simply restoring a recent backup of your 3G/3GS to your new iPhone 4 will hook you up.

Just backup 3GS with iTunes. Make sure the same number sim card is in your iphone4, iTunes will recognize it's a continuation and copy everything back onto your iPhone 4.

Originally Posted by asdttk

You can use iTunes or Outlook .Or you can get back your iPhone data in just few
clicks. iPad/iPhone/iPod Transfer is an idea solution for backuping iPhone content. This profesional iPhone backup tool can help you back up iPhone SMS,contacts, call list, songs, videos, books, photos and so on to computer or iTunes.
Good luck.

How to Backup iPhone SMS
Step 1 – Connect your iPhone to the computer with the USB cable.
Step 2 – Open iTunes (it it does not automatically open when the iPhone is connected to the computer).
Step 3 – Choose your iPhone model from the list under the “Devices” section of the left-hand menu on the iTunes main page and right-click the phone. Then, click “Back Up” to backup the iPhone’s SMS messages and other data to the computer.

Thanks for the advice. Doesn't seem to difficult. Even for a dinosaur like me.

I am trying to get my SMS,contacts and pictures on my iPhone to be put either onto my computer or onto iTunes and I don't know how to do this.
Any help or advice would be greatly received.
Thanks in advance.