This page of the Days Gone game guide contains information on how to acquire a crossbow. This is a very useful weapon, especially when it comes to killing opponents silently, and, moreover, Deacon can recover some of the bolts fired after unlocking a particular skill.
The good news is that you do not have to traverse the game's world in search of a crossbow or collect credits to buy it from one of the traders. The crossbow is automatically awarded through progress in the main storyline.
You can pick up the basic Crossbow model right after you have completed the series of introductory missions, more specifically, after Deacon and Boozer reach the O'Leary Mountain Safehouse for the first time. You can loot the crossbow from the gun locker - it will be located in the special weapons tab.
Do not forget to make bolts through the Survival Wheel. Luckily, this is a very simple task - you must have 1 piece of both Scrap and Cedar Sapling. Saplings can be picked from small trees which grow in almost every location within the game's world (you can see an example of the plant in question in the picture above).
It is worth mentioning, that in the later stages of the game, you will also unlock other types of bolts, e.g. ones that cause opponents to suffer hallucinations.
You can collect the upgraded, Drifter Crossbow model shortly after Deacon and Boozer complete their journey to the southern part of the map, specifically to Iron Mike's encampment in Lost Lake. This weapon will be granted to you after completing the storyline mission titled We've All Done Things. It is worth replacing the regular crossbow with the new model, as it has much better statistics (including, e.g. the damage it inflicts).