The traditional film rental solution is to drive to a store, browsing over what is currently in stock, make selections and leave. The DVDs are available relatively quickly, if you don't know what might be good and the ability to look through a selection is very handy. It may not be terribly convenient to make the trip, and there are limits to what each store can hold. This means it may be hard to find what you want in stock, with hot movies available in numbers to meet expected demand, and older movies pared down to meet the demand as well. One potential annoyance is the return. After you've picked up your film, you will have to return it. If it is late, there will be late fees, so you are saying, when you rent a movie, that you expect to make another trip out to the rental store within a couple of days. Sometimes, for whatever reason, this can be a problem. Sometimes the store hours can also be a limiting factor.
Netflix is one of the real success stories of the internet. You can visit the website, sign up for a plan and never enter a store. With an option for a $10 plan that allows you to keep a movie at a time, to a $25 plan that allows you to keep four rentals at a time, you can add DVDs to your queue on the website and they will be mailed to you with a postage paid return envelope. It does take as long as the mail takes, typically one to three days. This is a good option for busy people who don't want to waste their own time.
Blockbuster has attempted to create a mid-way point between these, with mailed movie rentals which can be returned to a convenient Blockbuster store rather than waiting on the mail each way. While this combines some of the strengths of both options, it also combines some of the weaknesses.
Redbox is an interesting option. Essentially a movie vending machine, the user selects a movie from those in the machine, pays with a credit card and takes it home. The $1 price is great, but there is a late fee if not returned by 7PM the next day. You can check the contents of the various boxes over the internet, since there is no guarantee that a given movie is in a given redbox when you arrive. This isn't a bad plan for a weekend movie source, but isn't for those who are picky and want to see a specific movie.
It is possible to rent movies online and have them delivered digitally, but right now no major studio has signed on over piracy concerns. Thus this is currently restricted to movies that simply aren't going to be in a theater anyway. Many of these use digital tricks to ensure a movie is unwatchable after the rental period.