I made a butcher block workbench for my garage several years ago. You do need a planar to do a neat job but I suppose one could get by with a sander and lots of sandpaper.
Get your wood and cut it into strips. If you are making an end grain butcher block, then you have to cut those strips to the depth of your block plus extra for sanding/planing. Glue together making bigger and bigger sections. In my case, my planar can only handle 12" stuff so I had to make three completed sections 12" wide and then glue them together at final assembly. Since I had no option to plane the entire butcher block as one unit, I took care to get the show face as flush as possible to minimize the sanding afterwards. All told it took me a couple weekends in the garage.
I made it out of some douglas fir boards that had been discarded because they were too checked to use for whomever had bought them. By cutting them into strips, I was able to discard the checked portions.
Actually you do not need a planer and can do larger sections. If you have a level surface you can use a set of parallel sided and identical height boards as rails on either side, then you place a router sled across the rails (and over the surface), and finally you run a router with a flat cut bit back-and-forth in the sled).
This may require a little more finishing sanding, but can handle wider pieces and if you already have a router the sled and rails are cheaper to make than buying a planer.
I would be highly skeptical of using this method for so large of a surface. First, finding straight enough material to use for rails on either side and then having a sled stiff enough that your force holding the router into the material and keeping router vibrations to a minimum to reduce chatter marks on your surface. I'm not saying it can't be done this way because I've used this method for much much small projects, but in my opinion, the most efficient way to do this project yourself it to buy, borrow or rent a planar.
I disagree, sometimes a board is too big for a planer, such a when my FIL used this for his counter tops (which was bigger than anything I have used it for), even having a planer in his shop. (well at least a 12-13 inch planer you are likely to find in a home shop); further it eliminate any small differences spots the block was glued after the bundles were planed.
Finding a material flat enough for the rails is really not a problem; you can square up two side of a board using a table saw, a jointer, or a jointer and planer and if you do the same step to each board before proceeding to the next then the rails will be the same size. Or just squaring the edges and ripping a couple prices of plywood on a table saw. In the end you may have to check the level of your work surface and shim as needed.
A plywood sled with a reenforcing ribs, when used with an appropriate thickness plywood, has been more than stiff enough to handle the force I have used for any span in the past. Shallow passes aid greatly in reducing chatter.
I will always use my planer for an item that can be run through it one pass as it will result in a surface that requires slightly less sanding, but if I were planing something that the end product is to be a flat surface I would use the router sled method. In many cases it can also be constructed out of scraps that are lying about the shop, which is quite handy if someone owns a router, but not a planer (like I did for several years).
I can see the benefits and drawbacks to each method, I simply wanted to point out to the original poster that a planer is not an absolute necessity for the project.