You do not need a birthday, a holiday or a complete account of your life to write a letter. A small thing that reminded you of someone is enough. The page can hold one story, a few questions and a familiar sign-off.
Begin with a shared detail
Write about a place you passed, a meal you made or a sentence you read that brought the person to mind. Specific details give the reader somewhere to stand. I saw the first leaves changing beside the old bridge is easier to enter than a long explanation of why you have not written.
Use your usual voice. A letter can sound like a conversation with a little more room between the sentences.
Tell one small story
Choose something that happened recently and describe it in a few lines. What did you see or hear? What surprised you? You can leave out the parts that do not help the reader follow it.
Ask a question you actually want answered. It might be about the book they mentioned, a project they were beginning, or the view from their window. One thoughtful question is enough.
Let a short letter be complete
A single sheet or postcard can hold a complete gesture. End when you have said what you meant to say, rather than adding paragraphs to fill the paper. Leave a little space around the writing so the page is easy to read.
Check the address with the recipient and the current posting requirements with your local postal service. Keep private information off the outside of the envelope beyond what delivery needs.