Try turning the headlights on, and then turn the ignition key to the start position. If the headlights go out or dim way down when the key is turned to the start position; it means that either your battery is discharged or has failed; or the battery cable connections at the battery posts are corroded. Corroded battery cable connections will often pass enough current to run the dash lights and small accessories; but will be unable to conduct the high current required by the starter. It is recommended to use a professional type battery cable service tool to clean the cable clamps and battery posts. The corrosion must be scraped off with the tool, until a shiny surface is present on both the posts and the inner surface of the clamps.
If the cable conections are not the problem; the battery may have become discharged if a light or other accessory was left on. Or, the battery may have sudenly failed from age. A discharged battery can often (but not always) be revived by charging it with a battery charger. It requires a charger with at least a 6 amp charging rate to recharge a dead battery. Charging usually takes about 10 hours. If a battery remains weak after charging for 10 hours or more; the battery should be replaced.
If the headlights do not dim when the key is turned to the start position; then something is preventing power from getting to the starter. This usually is caused by a neutral safety switch that is either defective, or else the gearshift lever is not in neutral or park. Try starting it in the park position and also in the neutral position. Sometimes it will start in one of those positions; but not in the other.
You can also jump start the car with jumper cables connected to the battery of another car. BE EXTREMELY CAREFUL TO ONLY CONNECT THE CABLES FROM NEGATIVE TO NEGATIVE, AND FROM POSITIVE TO POSITIVE. SOME BATTERIES HAVE THEIR TERMINAL POSITIONS IN DIFFERENT PLACES; SO IT IS NECESSARY TO FIND THE PLUS AND MINUS MARKS ON THE BATTERY TO BE SAFE. Reversing jumper cable connections is a sure way to destroy either the fusible links, or the alternator (or both). If jump starting gets it going; this indicates that the battery had been too weak to start the motor by itself, and confirms that nothing else is wrong with the car.
If it will not start from a jump start; using good quality cables with tight connections; then either the ignition switch, the neutral safety switch, the starter solenoid or the starter motor is defective.