These tips are for Americans -- I have no idea how UK citizens (or anyone else for that matter) can get an invite.
Start Early and line up your sponsor ahead of time:
We had no idea what the procedure was (my brother, who is living in the UK said, "Just write the embassy a nice letter, saying you have never been to Ascot before and they'll send you the tickets" -- it ain't that easy David!). Remember your sponsor needs to be a "Senator, congressman or a professional person of any nationality (e.g doctor, lawyer) or one who holds a position of responsibility in your local community or local government, where you reside", and the sponsor must provide both a letter of recommendation and sign the form stating "I have known this person for X years" -- I don't have that kind of relationship with any of my Congressional delegation, which is why we got the friend of my father. The embassy says that tickets are allotted on a "First come, first served" basis, but it is my feeling that the quality of your sponsor might have some influence your position in line. Either way, get your sponsor lined up before you write the embassy, so you can turn the process around quickly, as the original form from the embassy (not a copy) has to be returned to them with the recommendation letter.
If you really want to go, buy "Grandstand and Paddock" tickets as a backup
"Grandstand and Paddock" (General Admission) tickets go on sale at the first of the year, and sell out (especially for Ladies day) quickly. Buying them as a backup makes sense, especially since there is a vigorous "resale market" on the walkway between the train station and the track, despite the declarations of the Ascot Authority that ticket resale is prohibited and that "Persons acquiring tickets from ticket touts may be refused admission". As the "ticket touts" operate in full view of the local police, I have to assume that scalping isn't illegal as it is in most of the US. Anyway, if you really want to go, buy Grandstand tickets and, if you don't need them sell them to one of the ticket touts and get your money back.
Plan Monday carefully:
The vouchers from the embassy are handed out on the Thursday, Friday and Monday immediately before the meet (which is Tuesday -- Friday). If you arrive over the weekend, as we did, it means that on Monday, you have to go to the Embassy (to pick up the vouchers), then to St. James' Palace (to exchange the vouchers -- and £160 -- for the enclosure badges) and pick up your formal wear, assuming you don't own a set of morning clothes (btw I recommend Moss Brothers). This can be long day, especially if you are still jet-lagged. We compounded this by going to "Phantom of the Opera" that night, and on Tuesday, we were dragging.
White shirts aren't necessary
While Moss Brothers guide to formal dressing says that only white shirts are worn with Morning dress, it isn't de regeur, many of the gentlemen (in both enclosures) were wearing colored shirts, including yours truly, once I discovered that fact. Also don't rent the basic, boring grey vest (which I'm wearing in the photo above) if you don't need it, find something to match your lady's outfit.