New kitchen faucet water lines don't match old ones

Okay, I live in a about 15 year old house (trailer, technically). I needed to replace my faucet so I bought one that had the pulley-spout sprayer. It seemed nice, but i went to install it and realized the water lines do not match up at all. The new one has 3/8 inch connectors that screw on. But the old one had plastic pipes (aboutt 1/2 inch that connected directly to the handles of the last faucet) that came up from the water knobs on the floor. I took the plastic pipe off of the water knob because i assumed that it would have a place to screw the new one in. But it turns out that the spot on the water knob was completely smooth and had no place to screw anything on or into it. I have no idea how to use the faucet.
I was told it was very bad that the clamp was removed and that I would have to buy a tool to add new pipe to the water spout and that i would need to buy some type of shark/alligator female clamp to the pipe so i can screw the new ones in? I don't really know

That looks like Uponor expansion PEX. The tools to work with it are not cheap, probably not worth it to buy the tool for this one project.

Well, it was already removed from the valve, so a new PEX clamp would have to be put on wouldn't it? And yeah i definitely do not have the money to purchase the equipment for this