This is a page in Russian containing some advice of how to write a Latin letter, at the bottom of it you can find a few samples of letters. And I'm going to summarize the recommendations.
1. The salutation is generally in the third person:
Gaius Licoppe Sebastino Conoir salutem plurimam dicit.
Sodalibus in Latinitate odservandissimis salutem plurimam dico. (1st person, rare)
The formula of salutatations is usually based on the expression
salutem dare (dicere, nuntiare), and since it's quite common, it is very often abbreviated:
Sal. – salutem (dicit)
Sl. pl. – salutem plurimam (dicit)
s.p.d. (sl.pl.dc.) – salutem plurimam dicit (or
dat)
s.d.q.p. – salutem dicit (dat) quam plurimam etc
At the beginning of a letter the abbreviation
S.V.B.E.(E).V. – Si vales bene est, (ego) valeo.
often can be found. These formulas are traditional, but in principle it's possible to begin a letter directly with an address:
Domine mi honoratissime,…
Pater Domine Caelestis,…
2. Address
Latin lacks for a special form of the courteous address, that is the pronoun
tu is constantly applied. In order to show respect this pronoun as well as the words that depend on it can be capitalized:
Deus Te Tuosque tueatur!
At that such words as
Pater,
Spectissimus,
Carissimus [also
peritissimus,
illustris,
doctissimus,
optimus - Q] can be used. The adjectives often are in the superlative (although not necessary).
Non-Roman names are often latinized. Don't forget the vocative!
3. The farewell
A Latin letter is usually concluded with wishings of health and prosperity:
Vale, vige, vire, flore!
Vive valeque!
Cura, ut optime valeas!
Dies sint tibi laetitiae ac successuum pleni!
Curet Deus, ut quam optime valeas!
Te tueatur Omnepotens per annos innumeros!
Angeli sint tibi prope!
Superi te tueantur!
...
4. The subscription
Tuus Nicolaus
Tuus et Vester Аntonius
Totus Tuus Andreas
Amicissimus tuus Robertus
In caritate tuus…
Sincere tuus…
Medullitus Te salutat…
Te amplector…
...
5. The date
In a Latin letter the city / town (don't forget the locative!), the day of the month, the month and the year are commonly stated. It is preceded by a form of the verb
dare:
dabam (sc. epistulam),
datum,
data (sc. epistula):
Datum Romae die 6 Iunii a. D. 1999.
Data Aponi die 27 mens. Aug. anno 1998.
This form is used at the end of the letter before or after the subscription. But if the date is at the beginning of the letter, it is abbreviated as possible:
Kal. Iul. a. MM (Kalendis Iuliis anno MM)
Alexandriae, d. Iun. XXV a. 2000.