I made the switch from an iPhone 10 days ago. While all the above suggestions are good, I think you should plan on spending the first few days setting up the phone and figuring out how to use it like you did your iPhone. Specifically:
1) If you have not already done so, get a gmail account and move your contacts to google (it will be much easier this way).
2) Go into settings and set the default ring tone, even if you keep it the same, learn it LOL. Next set the ring tones for other people who have special ringtones on your iPhone. They will be different so you need to learn them. The alternative is to find those ringtones from your iPhone in MP3 format (they are in m4r format on the iphone which is not useable) and load them onto the phone. Google android ring tones for information on how to do this.
2) Setup notification for text messages. Personally I liked the default sound and method, but it took a while to realize that new sound was a message on MY phone.
3) Setup you e-mails. Then set up alerts! Again, you need to get used to the new notifications because otherwise you won't realize it's your phone.
4) Setup your social network connections (download apps if needed) and then set up alerts!
5) Setup visual voice mail (you need to download the app).
6) Rearrange things on the home screens to get your most used apps clustered together (like you did on your iPhone)
7) Spend some time using the base functionality (calls, messages, texts, e-mail). There is a learning curve, and in the beginning you will NOT be happy. iOS does do some things nicer, not necessarily better, but definitely smoother. For example you can't get into voice mail from the phone app. After a while you will get used to the Android way, but you will have doubts/issues at first.
NOW you are ready to play!

Follow all the advice of previous posters to start really having fun!
CAVEAT!!! The current version of Skype does not work on the S3! From what I have read it has not worked in months. You will need to find a work around. Also, the battery life without tweaking is shorter than what you are used to with the iPhone. This is especially true when you first get it and have it running all the time as you play with it. Expect to have to charge it one or more times a day until you get things going. If you are going on a long trip without access to power, bring along something, like a laptop, that can charge it. I personally bought an external rechargeable battery with a USB to micro USB cable (one way charges the external battery the other way charges your device). It's good for any portable device (even iPads) so keeping this one thing around is your emergency backup for any device you have.