Keyboards don't have one wire for each key. They have a couple dozen wires, and each key triggers a unique combination of those wires.
http/en.wikipedia.org/wiki/Computer_keyboard#Control_processor
When you get a short in a wire, or a key starts to trigger an adjacent wire, you start to get wrong and phantom keystrokes like you're experiencing.
Unfortunately, the cost of diagnosing the problem much less fixing it is a lot higher than simply buying a new keyboard. If you want you can try blowing out the keyboard with a can of compressed air - maybe some dirt is causing a short between some of the wires. But most of the time I've seen this problem, it's been from liquid being spilled into the keyboard.
Fortunately, most laptop keyboards can be bought on eBay for a reasonable price ($15-$50). Some are direct from the manufacturer in China (the real manufacturer, not your laptop brand name), others are used (but working) keyboards pulled from laptops where another component died. Most laptop keyboards are also fairly easy to replace. If it's a popular model, a Google search for disassembly instructions and videos should show you how to do it.
For an immediate remedy, plug in an external keyboard.