Registering with CORES: The first thing that needs to be done before filing an online application for a vanity call is to register with CORES. As stated on their website: "If you wish to conduct business with the FCC, you must first register through the FCC's COmmission REgistration System (CORES). Upon registration, you will be assigned a FCC Registration Number (FRN). This number will be used to uniquely identify you in all transactions with the FCC."

Registering with CORES can be done by clicking here and following the online instructions.

Become familiar with valid call sign rules: It should come as no surprise that all call signs are not created equal. Just as your particular amateur radio license entitles you to only operate within certain frequencies, your license also only entitles you to particular call sign groups and there are very specific rules associated with each group. The following text was taken from the FCC's site, the complete text of which can be found here. I would highly recommend that you follow the link to the sequential call sign system and thoroughly familiarize yourself with the information found there before you file your first application for a vanity call.

"A call sign is normally assignable two years following license expiration, surrender, revocation, set aside, cancellation, void ab initio, or death of the grantee. Where a vanity call sign for which the most recent recipient was ineligible is surrendered, cancelled, revoked or voided, the two-year requirement does not apply. Refer to the Sequential Call Sign System for how call signs are sequentially assigned and the grouping and geographic region attributes of each call sign.

"The following call signs are not available for assignment:

1. KA2AA-KA9ZZ, KC4AAA-KC4AAF, KC4USA-KC4USZ, KG4AA-KG4ZZ, KC6AA-KC6ZZ, KL9KAA- KL9KHZ, KX6AA-KX6ZZ;
2. Any call sign having the letters SOS or QRA-QUZ as the suffix;
3. Any call sign having the letters AM-AZ as the prefix (these prefixes are assigned to other countries by the ITU);
4. Any 2-by-3 format call sign having the letter X as the first letter of the suffix;
5. Any 2-by-3 format call sign having the letters AF, KF, NF, or WF as the prefix and the letters EMA as the suffix (U.S Government FEMA stations);
6. Any 2-by-3 format call sign having the letters AA-AL as the prefix;
7. Any 2-by-3 format call sign having the letters NA-NZ as the prefix;
8. Any 2-by-3 format call sign having the letters WC, WK, WM, WR, or WT as the prefix (Group X call signs);
9. Any 2-by-3 format call sign having the letters KP, NP or WP as the prefix and the numeral 0, 6, 7, 8 or 9;
10. Any 2-by-2 format call sign having the letters KP, NP or WP as the prefix and the numeral 0, 6, 7, 8 or 9;
11. Any 2-by-1 format call sign having the letters KP, NP or WP as the prefix and the numeral 0, 6, 7, 8 or 9;
12. Call signs having the single letter prefix (K, N or W), a single digit numeral 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and a single letter suffix are reserved for the special event call sign system.

Using the Universal Licensing System (ULS): Although you can file a request for a vanity call the old fashioned way, filing a paper form request, I would recommend that you file your request online. If you prefer the old fashioned way, you can find information on how to do that here.

You will also find information there on how to file online using the ULS. I have reproduced it here for your convenience.

Go to the Universal Licensing System, select Online Filing, and do the following:

1. Login to the ULS License Manager with your FCC Registration Number (FRN). Note: Tax Payer Identification Numbers (TINs) can no longer be used to login to ULS, effective December 14, 2003.
2. From your License At A Glance page, choose the Request Vanity Call Sign link on the right hand menu called Work on this License.
3. Answer the Applicant Questions, and click Continue.
4. Select Eligibility Click in the radio button to the left of the eligibility requirement under which you wish to apply for a vanity call sign:
   • Former primary station holder You are eligible to have the call sign which appears on your primary license displayed on your new vanity license if you are a former primary station holder.
   • Close relative of former holder You may display the call sign of a deceased spouse, child, grandchild, stepchild, parent, grandparent, stepparent, brother, sister, stepbrother, stepsister, aunt, uncle, niece, nephew, or in-law on your primary station license.
   • Primary station preference list You may request one or more call signs that you provide in the correct Commission format in the order of your preference. ULS will validate the format of each call sign on your list in turn and select the first call sign in the correct format which is not already assigned to another licensee.
   Note: You cannot receive a vanity call sign from a call sign group for which your operator class is not eligible. For example, if you are operator class T (technician), you can only receive call signs from groups C & D. If you request a call sign from groups A or B, your application will be dismissed by the Commission.

   After making your choice, click the Continue button.

5. On the Licensee Information page, review and update all of your licensee information. Make any corrections that are necessary. You must keep your address of record current with the FCC. This address will be used to mail you all official correspondence including your license and related information. When ready select Continue.
6. On the Summary page review the information you have entered. If you wish to make additional changes, click the Edit button next to the section of your application you wish to Edit. You will be able to return to that page of the application. Make the desired change(s) and select the Return to Summary button.
7. When ready to submit your application to the Commission, choose the Continue to Certify button.
8. After reading the certification, enter your first and last names and title if appropriate in the boxes at the bottom of the page. You MUST sign the application. When finished choose the Submit Application button.
9. From the ULS Confirmation screen, we recommend you print a copy of your application and/or the Confirmation screen itself from your web browser.

   Note: The address and contact information you have entered in CORES registration will not be automatically associated with your licenses. To change the address or other contact information on your license, you must update your information in ULS or submit Form 605 (edition date of March 2001 or later) manually.
   

After submitting the application form, you will receive a file number and the filing fee will be displayed. Click on View Form 159, select Form 159 button, and then choose to pay by credit card online. If you are not paying online, print out and mail Form 159 along with your payment by check or credit card to:

Federal Communications Commission
Wireless Bureau Applications
P.O. Box 358994
Pittsburgh, PA 15251-5994

Note: If you submit an application in ULS and do not make fee payment online, the rules require that the FCC receives your payment within 10 days of your submission date.

Obtaining a refund: Obtaining a vanity license is always a gamble, by its very nature, even if you do everything right. Quite often you will find that someone else has filed for the same call you have requested and whether it is awarded to you or them is a random process with no guarantees. Fortunately, the fee for filing an application that is subsequently dismissed is refundable.

You can request a refund by submitting an Online Help Request. Alternately, you can send a request by regular mail to:

Federal Communications Commission 
1270 Fairfield Road 
Gettysburg, PA 17325-7245

The requested refund should contain the following information:

Your Name, Call Sign
Address
Taxpayer Identification Number 
Application Date:  XX/XX/XXXX

If you filed electronically then I would also recommend providing the following information:

Remittance ID: XXXXXX
Authorization Number: XXXXXX
FRN: XXXXXXXXXX
FCC CODE 2:  XXXXXXXXXX

The "X's" are provided just to give you an idea of the format and number of digits to expect when looking for the information on the vanity application.