If your toilet won't flush properly, there is likely a clog in the pipe. You can often dislodge a clog of this nature by using a plunger. Be sure to use the plunger consistently until the basin of the toilet drains on its own; flushing the toilet without waiting for the water to drain could cause the basin to overflow.
Shower and Sink Clogs
Most shower and sink clogs come from hair and other debris washed down the drain. You can prevent clogs in large drains by installing traps that prevent large items from being flushed down.
If you need to clear out a clog, you can use a hand tool like an auger; some hardware stores also sell drain cleaning tools you fish into the drain.
Please do not use chemicals to clear your drains as they could damage your plumbing system.