Toilet Problem- Water not able to flush at all
It sounds like there is a blockage somewhere.  It could be right at the toilet (waste gets trapped in the bends that form the built-in trap).  If the material gets past that, it typically makes it to the sewer line.  However sewer lines can get blocked between your house and the tie-in to the main sewer line (some old pipe materials were prone to breakage, rocks in the backfill can cause breakage, etc., then dirt or roots get into the pipe and block it).  

If the problem is the sewer line, it will affect all of the plumbing in your house.  If it is the cause of water not going down at all, or only at a trickle, in that toilet, all toilets, sinks, bathtubs, etc. will drain very slowly).  If you have a washing machine that discharges into a utility sink, that would be a place where a sewer problem would likely be visible.  

A simple way to test this is to fill all your sinks and bathtubs, turn on all inside faucets, and have people stationed at all sinks, tubs, and toilets to release the water from the sinks and tubs and flush the toilets at the same time on a signal.  If everything drains at a normal speed, the sewer line is not the problem.  (If it is the sewer line, post a new question because that's a subject all its own.)

If there is a problem with just one, or just a few, of the plumbing fixtures in addition to that toilet, the blockage may be where several discharge lines connect within your house.  A plumber will be able to figure out the location and will have the tools to clear it.

If the problem is at the toilet, itself, there are a number of ways to clear it.  If there is any chance that it is not normal, flushable waste (like a young child tried to flush a toy), you might want to call a plumber, because normal solutions to clear a clog will likely just make the problem worse and harder to solve.

The typical clog is human waste and toilet paper (and sometimes feminine pads that are not intended to be flushable).  The problem is usually the toilet paper or pad.  The pads are not designed to break up, so if it is likely to be that, the first solution is to try to use a plumbing snake to pull it back out.  If that doesn't work, try to break it up with the plumbing snake.  Which brings us to the standard solutions.

There are three basic approaches to toilet clogs: plumbing snake to break up the clog and push it past the point where it is caught, plunger to apply pressure to force the clog past, or breaking up the clog "chemically".  Any of these approaches might require repeated tries to clear a stubborn clog.

The snake is pretty self explanatory.  One word about plungers--you need to use the right type.  There are two styles of plungers.  One looks like a big suction cup, a dome with a flat edge.  That style is for sinks or basins and won't work well for toilets.  Toilet plungers have a "bell" and then a snout that fits into the discharge well at the bottom of the toilet.  You need that style for it to be effective.

I use the term "chemical" loosely.  There are caustic chemicals (typically containing lye), that dissolve the toilet paper, breaking up the clog.  Some contain concentrated bleach as the active chemical.  Hot water and liquid detergent is at least as effective.  For any of the "chemical" approaches to work, the toilet needs to be draining, even if very slowly.  If it is totally blocked and not draining at all, use one of the mechanical methods.  If you try caustic chemicals and then need to use mechanical methods, you've created a nasty environment to work in or get splashed by.  You can try the hot water method if you use something like an old pot to remove most of the standing mess so that the toilet bowl is almost empty (personally, I'd just use one of the mechanical methods, instead).

The hot water method: fill a large pot with water and bring it to boiling on the stove.  With the toilet bowl almost empty, squirt some liquid dish detergent into the bowl, then carefully pour in the hot water (be careful not to splash yourself).  Refill the pot and get it heating for the next application.  When the water has trickled out of the bowl so that it's almost empty again, repeat the process.  This normal requires several applications for a stubborn clog, often three or four in a row.  It takes the hot water and detergent time to work its way through the clog.  But it's a pretty "clean" solution that requires little effort and is very effective.

If you try the hot water method say six times in a row and there is no visible improvement, it probably means that it isn't a normal clog.  You will need to try one of the mechanical methods or call a plumber.