*Blue plastic "double" electrical box (for household wiring) $1
*Standard electrical outlet and outlet/switch faceplate $2
*12 volt transformer and full-wave bridge (cut up an old one that you are not using. $6 for Jameco #100095)
*Power cord (cut up an old one)
*558 timer chip (Jameco #27457) $1.20
*Solid state relay Kyotto KB20C02A (Jameco #175214) $6.55
*7808 or 7809 voltage regulator (Jameco #876352) $0.56
*two 100K pots (Jameco #29103) $2.18
*two 3,300 uF capacitors (Jameco #93666) $1.22
*PN2222 transistor (Jameco #178511) $0.12
*perf board, wire, maybe a 16-pin DIP socket, misc caps and resistors $2.00
Total parts cost is about $23. Here's a link to Jameco
This circuit does not provide the "soft start" that many commercial wavemakers tout. These motors likely use shaded poles for starting, and a soft-start controller would have to control the frequency of the AC power, not just the voltage. I find it pretty unlikely that this is what any wavemaker does, and for the price they charge, it's probably cheaper to buy a new powerhead every year! I haven't used my wavemaker long enough to know if it will kill the powerhead. I'm using an Aquaclear powerhead, and it clicks loudly upon startup, but there is no chatter. I may make another post about modifying the impeller to cope with the repeated startups.
I've experimented with using dimmers, current-limiters, etc, to control the speed of powerheads. The speed can only be reduced %10 or %20 before the motor stalls. It's not really practical without control over the frequency of the AC waveform.
The Solid-state relay in this circuit has a current limit of 2A. This mean it can control up to about 200W of powerhead.