How do I know how many enemies I need for the Genocide Route?

The Ruins save points don't give a kill counter, only later ones do.

You need to keep killing more monsters until battles give the message "But nobody came..." This must be done before approaching the boss monster for the area (at the point where you would normally fight them), even if you could normally turn back without fighting them. As long as you're on the Genocide route, save points checked outside the Ruins will give you a count of the number of monsters you have left to kill in the area. The count of monster kills for each section, followed by the name of the area boss, is as follows.

• Ruins: 20 kills (Toriel)
• Snowdin: 16 kills (Papyrus)
• Waterfall: 18 kills (Undyne the Undying)
• Hotland/Core: 40 kills (Mettaton NEO)

You don't need to kill every enemy you encounter, you're allowed to flee from or spare enemies, except for a select few), but you must also kill every unique enemy you encounter. This includes Shyren and Snowdrake. Although the Shyren encounter will happen even if the kill counter is depleted, the Snowdrake encounter will not and can ruin a genocide run.

Note that the requirements is in the number of kills, not battles, so battles with more enemies are more efficient for quickly reaching your goal. You will know that you have enough kills when interacting with a save point simply produces the message "Determination". If you ever leave the Genocide route, there's no way to get back on it without reloading a save from before you left the route.

Source: http://undertale.wikia.com/wiki/Genocide_Route#Requirements

While you are in the ruins the "Determanation Star" or "Save Point" does not say how many monsters you have killed or have to kill. The best way to keep track is to count in the ruins. Unlike the ruins, the "Save Points" from Snowdin will then on say how many monsters you must kill. To know you are on the genocide in the ruins is if you kill Toriel in one hit. She will also say, "You really hate me that much?"

Toriel: 20 Papyrus:16 Undyne: 18 Mettaton:40

As of the last boss, Sans, you do not need to kill anything. DO NOT start a boss fight before you have killed all the monsters, Sans is the ONLY boss that does not need any kills before his boss fight. Other than than Sans if you miss one monster before a boss fight you fail.