Finding free car repair manuals online can be a challenge. This is particularly true for newer cars since most of the manuals are not yet published online. However, if you have an older vehicle, you may have some luck at one of the following sites:
Autozone Free Vehicle Repair Guides
If you sign up for a free membership at Autozone, you can access a section on their website where they offer free auto repair manuals. There is no obligation to buy anything, and no fee to register. The only downside is that they don't have manuals for every make and model, so you may not be able to find the manual you need for your vehicle -- particularly if it was made after 2007.
This site features free workshop repair manuals for a variety of different makes and models. The manuals are available directly in your web browser with no need to register or download anything. Again, however, the manuals tend to focus on older vehicles models from the 1980s to the early 2000s. If you need anything newer than that, you are pretty much out of luck. 
If all else fails, you may be able to find free repair manuals at your local library. They are usually located in the reference section. In many cases you won't be able to check them out from the library, but you can make photocopies of relevant pages. It is not a perfect solution, but it can work in a pinch. Also, you may be able to find manuals for newer vehicles by going this route.