How should I write a letter in Spanish?

As with writing a letter in English, it is important to adopt the correct register and tone for the person you are writing to.

To open your letter, use one of the following options, picking the best one to suit the tone of the letter. 

Querido _______: [This directly translates as 'Dear ______,'. It is fairly informal in Spanish, and so should only be used with people such as family members or friends. Note the use of the colon (:) rather than a comma (,) after the name. It is also important to change the agreement of 'Querido' to suit the person (i.e. querido for a male, querida for a female and queridos for multiple people.)]

'Estimado Señor _____:' [This is a more formal opening, which is good for using if you know the name of the person you are writing to, but are not close with them. As before, it is important to choose the correct agreement.]

'Muy señor mío:' [If you do not know the name of the person, this option translates as 'Dear Sir,'. Again, in changing the agreements to 'Muy señora mía', this becomes 'Dear madam,']

To close a formal letter, the most commonly used word is 'atentamente', although 'cordialmente' is also used (the latter in more casual contexts). For an informal letter, there are many options which can be chosen to suit your letter. 

Un abrazo - A hug
Besos y abrazos - kisses and hugs
con todo mi cariño - with all my care
afectuosamente - affectionately 
cariñosos saludos - kind regards

Whilst these are not necessarily phrases we would use in English, all of the above are perfectly acceptable closing remarks to make in a more informal Spanish letter.