The perf board is potentially pretty simple, but lets look at build a cpu against buy a cpu first. While it is entirely possible to build a Uno (I don't think you need a mega for this) on perf board (as the original person did) it doesn't usually make sense. For around $2 US you can buy from ebay a complete Arduino nano. On a board the size of about a 24 pin dip you get what amounts to (and more importantly programs like) a uno. To do the same on perfboard you need a 328 CPU $4 in small quantities from digikey, around $10 with the Arduino boot loader loaded in to it. Then you need a 16 meg crystal, a couple of caps, a socket various pins and bits. I doubt you will get away with much less than $20 and now you have to build it (so add in what ever your time is worth). Once that is done then you have to arrange to program it which is non trivial too. That $2 nano (which have all those plus the programming) looks much more attractive to me. As to building on perf board, go back to your version that has the schematic with no breadboard connections. In breadboard view delete the breadboard and replace it with one of the perfboard options from the core parts bin and wire up your circuit on the perf board instead of on the breadboard. Then copy the diagram in to real life perf board and solder it all together. They also make perf board that has the same pattern as the breadboard and you can just move your circuit from the breadboard on to the same places on the perfboard and solder it down.
Peter