The purpose of an LTE is typically to respond to an article that you support or disagree with. They can sometimes be used to comment on a current issue being debated by policymakers.
When working on an LTE, the rules are similar to an op-ed, only the copy is much shorter – roughly 150 to 250 words. In most cases, you will be pitching an LTE to a daily newspaper; almost all have contact information on their webpage describing how to submit your letter. Look at LTEs that the paper has run to see their format. The standard format is to begin your LTE by referencing the article you are commenting on, e.g. Re: “[title of article]” – and then make your case.