What is wi-fi?

Wi-fi stands for WIreless-FIdelity. It is actually a Local Area Network, but instead of using LAN cable, it use wireless.

If your old computer has USB ports available, you can buy a wi-fi USB donggle and plug in to your system. You will need a driver for your USB wi-fi device, a quick search in Ubuntu 'Additional Hardware' should give you the appropriate driver.

If your computer is a desktop and you have one PCI slots available, then you can buy an internal wi-fi PCI card and install it in your system. Of course you need a driver before you can use it, a search in the internet should solve this.

To connect to a wi-fi access point 'known as hotspot or wireless router' may need a few technical knowledge. In your case, try to ask the hotel management if their wi-fi use any encryption key and their wi-fi SSID name (This name is used to let you identify the wireless access point network, since many people has wi-fi router [like wired router, but this router is using wireless, it is pretty common in residential area]). Having that information, key them in to your system and you should be able to use their wi-fi service.

Do note that some (this is more technical) may ask you for MAC address, or assign you a static IP address.

Hope this tiny info helps you a little.

Some additional info:

"Could I just plug my internet cable into a wireless router and the wireless router will automatically pick up the wi-fi signal?"

If you have physical access to the router that provides the Internet connection (i.e., that is itself connected to the Internet), and the router has Ethernet ports for you to plug your computer into, then you should be able to connect to the Internet that way. But that would not be connecting wirelessly (i.e., not with wifi). You would just be connecting via Ethernet to a router that is also wifi-capable.

However, you are unlikely to have physical access to a router into which you can plug your computer, when you have wifi provided as an amenity.

If you are asking if you can buy a wireless router and use it to connect your wifi-incapable computer, through it, to a wireless network, the answer is no. Most wireless routers do not have this functionality. There is another kind of device, though, called a wireless bridge, that does this. If you buy a wireless bridge, you should make sure it supports the wireless network you will be using--that is, that is supports the specific standard (for example, 802.11g, or 802.11n -- those are just examples) that is used in your building, and also that it supports whatever kind of encryption (for example, WPA2) that will be used, if any. (You should also make sure a wireless network adapter, such as a USB dongle or PC/PCI/PCI-E card, is compatible with your network. I just emphasized that for wireless bridges, as bridges tend to be more expensive than wireless network adapters.)

Wi-Fi, often referred to as WiFi, wifi, wi-fi or wi fi, is often thought to be short for Wireless Fidelity but there is no such thing. The term was created by a marketing firm because the wireless industry was looking for a user-friendly name to refer to some not so user-friendly technology known as IEEE 802.11. Running my https://inshotproapp.com/ blog on wifi.