TextMe Up is a free service that works over your existing internet data plan (the same you use for email and web browsing) or any available WiFi.
You still have to check your phone operator contract for your data plan details, but if you have unlimited internet access from your smartphone, you won't have extra charge.
You need to have an internet connection to use TextMe Up.
It works on WiFi, 3G or 4G or Edge connections, whichever is available.