Basically, two choices for so-called “high-speed” – cable and telephone line. Wireless is a possibility, but you need to understand that there are two types of wireless: local and wide-area. Wireless connections require hardware in your computer. Local means your computer is within 50 feet of a wireless router that could be in a home or a so-called hot-spot. Wide area requires a different kind of hardware and will likely be pretty pricey to use. Wireless is always substantially slower.
Cable is technically superior to telephone lines, and is typically priced the same. Wild and irresponsible claims are made by both. There are huge differences. They vary from a low of 500 to a normal high of 50,000Mbps. Cable usually delivers 90% of the speeds promised. Telephone rarely delivers a more than 50% of speeds claimed and most commonly 20%. There are a few cases where the telephone company has installed fiber optic cable to a point on your street outside your home. In those cases, they can deliver the same performance as cable.
You will contract with an Internet Service Provider (ISP) who will be your connection. They will require you to rent or buy a modem which is a small box that connects to their service. If you want wireless, you will need a second box called a router. Some modems have routers built-in, but it is usually better to have separate modems and routers. If you have wireless in your home, ensure it is password protected, else your next door neighbour could be using your connection.