Best practice
This page covers a few of the conventions that apply in particular forms of writing. In many contexts, consideration of these points is superfluous. If nothing else, they represent good practice.
Yours sincerely or Yours faithfully
In a formal letter, it is customary to sign off with yours sincerely or yours faithfully. The rule that determines which one to use is below. Note that this is primarily a British convention, although it can apply elsewhere.
If the letter is addressed to a named individual, you sign off with yours sincerely. If the letter is not addressed to a named individual, you sign off with yours faithfully. One way to remember this is to think: if you don't know the name of the person you are writing to, you should have faith that it will reach the right person.
Examples
A letter that begins: Dear Dr. Smith,
Should be signed off: Yours sincerely,
A letter that begins: Dear Sir/Madam,
Should be signed off: Yours faithfully,
Ending sentences with prepositions
Prepositions are words like: in, on, beneath, over.
It is considered bad practice in formal writing to use a preposition as the last word of a sentence. Formal definitions can be found elsewhere.
Example
The sentence: A secure cabinet is a suitable place to store sensitive documents in.
Should, in a formal context, be written: A secure cabinet is a suitable place in which to store sensitive documents.
Split infinitives
The formal definition of an infinitive is long, boring and easy to find elsewhere. Happily, it's not hugely important in this context, because the rule can be understood without getting bogged down in technical details. We are considering phrases like to run, to eat, to write etc.
It is generally considered a bad habit, in formal writing, to place and adverb between the word to and the subsequent verb.
Examples
The sentence: I have to quickly drink my coffee because my flight is boarding soon.
Should, in a formal context, be written: I have to drink my coffee quickly because my flight is boarding soon.
The sentence: I believe I am going to easily pass my exam.
Should, in a formal context, be written: I believe I am going to pass my exam easily.