Well, there are several things you need to know first.
If you think that your Jewish friend is an expert in the Hebrew Scriptures (commonly called the ‘Old Testament’) and that makes you afraid to share – then let us assure you – you have nothing to fear.
Most (not all) Jewish people have never even read their own Hebrew Bible. Yes, rabbinical students have, but the typical Jewish person is very traditionally Jewish. That means they know Jewish traditions, but not necessarily what the scriptures say.
Second, be a genuine friend to them first. No, this is not using subterfuge, but a genuine love you should feel for one of God’s Chosen people.
Third, send an appropriate card. Instead of sending them an annual Christmas card, why not send them a Hanukkah card. Or even a card for the Jewish New Year called "Rosh HaShana". This shows them you care and is the proper heart attitude to have.
Fourth, when you talk about your faith, use Jewish terms like “Messiah” instead of the Greek term “Christ.” Did you know the two words mean the same thing, but in two different languages? “Messiah” and “Christ” both mean “Anointed” one. Therefore Jesus Christ really means Jesus the Anointed One (the Messiah).
Fifth, and most importantly, know why you believe by using only the Hebrew Bible (Old Testament). Share scriptures of the coming Messiah like Isaiah chapter 53. Google “Prophecies about the Messiah” and you will get many suggestions about where to look.