How can I build a cheap wood countertop?

Butcher block?

If so, all the wood will need to be cut evenly and be sanded if there’s any irregularities.

Use wood glue & double glue the sides & wood clamp together for a week.

Remove the clamps, sand off the glue, cut the edges if not true and wipe clean.

Then two full coats of waterproof polyurethane. Let dry 48 hours before using.

I am in the process of doing this, so I can't tell you for sure it will turn out like I am hoping, but I went to ReStore (the Habitat for Humanity supporting place where people donate leftover building supplies and stuff) and bought three solid wood doors wider and longer than I need (I have a TINY kitchen). My plan is to cut them down to the right sizes, sand them really well, and use several coats of spar varnish or some other water-resistant coating. I will be using drop-in type stainless sink rather than an undermounted sink to help minimize wood-water contact , but a farmhouse style sink would also be a good choice. The doors would need to be solid and flat (without panels).

Hi Pam, here's one idea

https://www.youtube.com/watch?v=F9oklkp5nbA

https://www.hometalk.com/diy/build/furniture/gorgeous-wood-countertops-anybody-can-diy-40606647