Many legal issues are different in various towns and cities, so you should double check with the city hall in your area. But normally what you should do is the following:

Before you get married:
1) Notify your employer and they will prepare your email address and business cards you may need for changing. All your contacts may need to be notified so they may reach you when they call.

2) When making reservations for your Honeymoon, plane tickets, or anything requiring ID directly after your wedding, make sure you use your current last name, your maiden name. Because you will not have changed your passport, drivers license, or other forms of ID yet. So be aware that all your other documents, such as credit cards, and ATM cards will still be in your old name.

Once you have gotten married then:
1) Apply for a new Social Security Card. In a couple weeks, when you receive your marriage license in the mail, you can go to your local social security office to fill out a form and get a new card or you can conveniently use an online form to apply on various websites.

2)Apply for a new Driver's License.
Either on your Driver's License or your ID card, you will wish to update your new last name. Various DMV's will ask for either the marriage certificate or your new Social Security card. You can find the application forms by going to your local DMV and asking for them or you can find them online.

Make a list of all the places your name would appear on a document or company. Here is a list of possible things that may help. Bank accounts, credit cards, order new checks, IRS tax returns, insurance policies, car leases or fiances, home mortgages, school loans, other bills such as cell phone, gym. Notify your accountant so they can figure out if you will have any new tax deductions.

You can find and simply fill out all these various forms and notices automatically and all at once on website services that will organize and simplify the chore of running around and doing it separately. Don't bother with Name Change Kits that require installation and wait time for delivery.

And lastly, tell people and use your new last name. It will take some getting use to but that's most of the fun.