Thanks for the question. I'll shed some light. There are two kinds of electric vehicles:
Full Electric - (i.e. Tesla Models, Chevrolet Bolt, Nissan Leaf) These have huge batteries lasting 150+ miles, with the largest batteries over 300 miles of total range.
Plug-In Hybrid (i.e. Chevrolet Volt, Toyota Prius Prime, BMW i8) These are "transitional electric vehicles" that were designed to bridge the gap between gas and electric. All automakers have these options available but they won't market them because it is difficult to explain to customers. These have small batteries (10-50 miles range) but a fully operational gas engine once the battery is depleted. In short, they are a Tesla on electric mode, but a conventional hybrid (i.e Toyota Prius) under gas mode. They can run on gas indefinitely, and take road trips just like a regular car. You never have to charge these if you are unable to find charging.
Now to your question - There are 3 ways to charge an electric vehicle:
Level 1: This is with a standard kitchen duplex outlet. All electric vehicles come with an adapter that will plug into any 110V outlet. Recharge rate is about 4 miles per charging hour. It takes 3-4 days to charge a fully electric car, and about 12 hours to charge a Plug-In Hybrid
Level 2: This is with a 240 Volt Charging Station. Most EV owners purchase this for their home. These are also found in shopping malls, parking garages, and airports. Recharge rate is about 20 miles per charging hour. It takes 8-10 hours to fully charge an electric car, and just 2 hours to charge a Plug-in Hybrid
Level 3: This is called "fast charging." These are usually found at rest areas. Tesla Superchargers are at this level, but are encrypted so that only Teslas can use them. Recharge rate is about 300 miles per hour. They can fully charge most electric vehicles in 45 minutes. Plug-in Hybrids cannot use these.
Most EV drivers do not charge publicly, with the exceptions being parking garages and road trips. Parking garage charging is usually "free" because it is included in the cost of parking. Outside of garages, the cost of public chargers is usually at least 5X more expensive than charging at home. They are owned and serviced by private companies, so they aren't well regulated. Also, it's common to go to a charging station and it is either broken, taken, or the spot is just blocked by a non-EV because someone is being a scrub.
Also, utility companies don't advertise this- but they have time of use power plans. This is useful for anyone without solar panels on their home. I have a time of use plan. Standard electricity for me was $.13 / KwH, but now I pay $.17 / kwH during the day and just $.06 overnight. My car has a 15 kW battery, so each charge costs about $1 and I get 53 miles of juice. A 100kWh Tesla would cost me about $7 to fully charge at home for 300 miles of juice. If you convert that it in $ it is roughly 150 MPG.