You can unlock V Bucks by completing challenges or purchasing them for real money. Once you have V Bucks, you can use them to purchase cosmetic items for your character in the Battle Royale lobby. Challenges are weekly objectives that grant you v bucks and XP when completed. The current weekly challenge is listed on the right side of your screen above the chat window.
How many V-Bucks can you get for $10? $15? $20? There are four tiers of V-Bucks available, with the higher tiers granting you more V-Bucks at a time. Check out the following chart to see how many V-Bucks each tier grants.