In-app purchases
Instead of having people pay for your game up front, you can offer a free game with in-app purchases (IAPs.) In this case the game can be acquired without spending a dime — give the game to the players, but offer in-game currency, bonuses or benefits for real money. Specific examples can include bonus levels, better weapons or spells, or refilling the energy needed to play. Designing a good IAP system is an art of it's own.
Remember that you need thousands of downloads of your game to make IAPs effective — only a small fraction of players will actually pay for IAPs. How small? It varies, but around one person in every thousand is about average. The more people that play your game, the higher the chance someone will pay, so your earnings heavily depend on your promotionactivities.
Freemium
Games that feature IAPs are often referred to a freemium — a freemium game can be acquired and played for free, but you can pay for extra (premium) features, virtual goods or other benefits. The word itself acquired negative connotations after big companies focused on creating games, the main purpose of which was to get as much money from the players as possible instead of delivering a fun experience. The worst cases were when you could use real money to pay for getting advantages over other players, or when they restricted access to the next stages of the game unless the players paid. The term "pay to win" was coined and this approach is disliked by many players and devs. If you want to implement IAPs try to add value to the game with something players will enjoy instead of taking it out and then charging for it.
Add-ons and DLCs
Add-ons and downloadable content are a good way to provide extra value to an already released game, but remember that you'll have to offer decent, entertaining content to attract people to buy it. A totally new set of levels with new characters, weapons and story is a good material for DLC, but to have enough sales the game itself has to be popular, or else there won't be any players interested in spending their hard earned money on it.