BMitch's solution will only work for pressurized water systems, which, while standard in the US, are not standard elsewhere, and it sounds like you have an unpressurized system where the water pressure is created by gravity.

If this is the case, go with ratchet freak's solution.  The only problem is getting all of the air out of the pipes.  The only ways that I can come up with to do this is to buy a regular ol' pump (if there is an existing drain valve) or buy a self-priming pump (more expensive.)

With a non-priming pump, it will look like this:
    
      ____________________
     |                    |          
     |                    B          
     |            ________|________ 
     |    _______|_               _|_______
     |   |       | |             | |       |
     |   |       | |             | |       |
     |   |       | |             | |       |
     |   |       | |             | |       |
     |   |       | |             | |       |
     P   |       | |             | |       |
     '---D_________|             |_________|
    
    P = pump
    D = drain
    B = ball valve
   

With a self-priming pump, it will look like this:

             __________
            |          |          
            |          B          
            P  ________|________  
      ______|_|_               _|________
     |      | | |             | |        |
     |      | | |             | |        |
     |      | | |             | |        |
     |      | | |             | |        |
     |      | | |             | |        |
     |      | | |             | |        |
     |__________|             |__________|

    P = pump
    B = ball valve

In both cases, the pumps will be pumping upward.  The water that they push up the pipe will flush out any air.  It may take a few minutes to manage this, but it will flush out any air bubbles in the pipes, allowing the water to siphon back and forth between the tanks.

In order to operate the systems, perform the following steps:

 1. If you're connecting to a drain valve (like in the first diagram,) then open the drain valve.
 2. Turn the pump on.
 3. Immediately open the ball valve.  (Recommended delay between steps 2 and 3: 3 seconds.)
 4. Wait 2-3 minutes.
 5. Close the ball valve (B).
 6. Immediately turn off the pump.  (Recommended delay between steps 5 and 6: 3 seconds.)
 7. If you're connecting to a drain valve, then close the drain valve.

There are only two requirements for the system:

 1. The pump needs enough "head" (how high it can push water)
 2. The pump needs a sufficient flow rate to entrain the air bubbles (shove them out of the bottom of the pipe)

In order to make sure the pump meets these requirements, you need to measure from the bottom of the tank to the top of the pipes shown in this diagram.  That's pretty close to the wost-case scenario in regards to how much head the pump will need.

Find out how much flow rate the pump needs to entrain the bubbles.  I don't know this offhand, but you should be able to find it by googling or asking a pump professional.  You will need to know the diameter of the pipes involved, as larger pipes will take more flow rate to entrain bubbles.  (1/2" pipe should sufficient for this purpose, as it doesn't really matter if it takes an hour to equalize the water levels.)

In fact, if you ask a pump professional, giving him the amount of head required, pipe diameter, and tell him that it must entrain the air bubbles, he should be able to recommend an appropriate pump within 5 minutes.

Anyways, if you want to figure it out yourself, you should have figured out the head and flow rate requirements.  All you need to do is find a store that sells pumps and ask for a pump that meets those requirements or ask for pump charts showing head/flow rate.  The charts will look like this:

          20 |
     H       |...
     E    15 |    '''..
     A       |         '.
     D    10 |           '
    (ft)     |            '
           5 |             '
             |_____________'____
                 0   1   1   2
                 .   .   .   .
                 5   0   5   0        
               FLOW RATE (GAL/MIN)

The chart shows a basic characteristic of pumping: that flow rate goes down as head goes up.  Find your head requirement on the left axis and trace a line horizontally to the right.  Where it hits the curve is the flow rate that the pump will put out at that amount of head.  I'd aim to overshoot your flow rate requirement by 10-20%.

If I had to guess, you should only need to run the pump for 2-3 minutes once a month or so to maintain the siphon.  The only way for air to get into the pipes that are part of the siphon system is the tanks are allowed to get very low or (a much more gradual process) of air bubbles entrained in the water pumped from the well get into the pipes or air otherwise falls out of solution.