As we develop range confidence we'll naturally want to drive farther from home. Obviously we'll have to use public charging stations, just like gasoline car drivers use public gasoline stations.
In online conversations, I regularly see people saying they never charge away from home. It's hard to judge someone else's choice, but I argue limiting your electric travels like this is not the best. These cars are capable of longer trips than a short distance circle surrounding your house, and the more you drive electric the bigger your gain.
Taking longer trips is simple, learn charging station locations, plan a trip using those stations, then jump in the car and go. The only complication is learning when you need to carry extra equipment.
The charging rate (3 kW, 6 kW, 120 kW, etc) determines our effective trip speed. For example the rule of thumb is that at 6 kW an average electric car gains 20-25 miles range per hour of charging. See Understanding charging rates and effective trip speed
The charging rate we need in any given situation depends on situational needs. If our electric car is in an airport long-term parking lot during a 2 week trip, it doesn't need to a normal charging rate (6 kiloWatt) because it'll be fully charged long before we return to unplug the car. That's really bad EV charging etiquette, since the charging station remains tied up during the entire trip. If the car is parked at the office, we'll have 8 hours (or so) during which the car can recharge, and a 6 kW station is probably not required. During a Road Trip, the charging rate needs to be as high as possible. See What charging rate do we need? “As fast as possible” isn’t always what’s needed
If we need to drive to a place with no charging stations? An electric car is just as dependent on charging stations as a gasoline car is dependent on gas stations. An electric car driver has the advantage of charging at any electrical power outlet, while a gasoline car can only recharge at a gas station. To drive where there's no charging stations, the electric car driver either needs to bite the bullet and drive a gasoline car, or else become proficient in guerrilla charging from any power outlet. See Can you drive an electric car away from charging network coverage areas?
Successfully using public charging stations requires maintaining memberships in multiple charging networks. See What charging networks exist? ChargePoint? Plugshare? See Known electric car charging networks around the world
While we have common charging standards, there's enough variation that we need pictures of the different equipment we'll be using. See A Field Guide to electric vehicle service equipment (EVSE's)
Often public charging stations charge usage fee's. See How do I pay for energy consumed in charging my electric vehicle?
Charging station networks need to make their profit, so that the network stays in operation. See How do electric car charging station networks make money?
Smart-phone apps are available showing available charging stations. See Smart-phone apps for finding electric car charging station networks
Not all charging stations are well maintained, and sometimes the charging cord gets stuck. There's a simple cure. See What to do if the charging cord is stuck, cannot be removed