Acquire a suitable bike to use. Remove the wheels, shifters, brakes and cables. I opted for this sturdy dual suspension mountain bike.
Design the mounting brackets that will attach the skis to the bike. I decided to make my brackets so the bike would sit just slightly lower than a conventional mountain bike.
Use trigonometry to calculate how long to cut the 2x4s and at what angles. The design for the front and rear brackets were not identical because the rear dropout spacing is wider than the front.
Cut the skis as necessary. I was using old downhill skis so I cut them to about 30 inches for quick handling.
Use decking screws that are at least 2.5 inches long to fasten everything together. This will ensure a strong connection between the 2x4s and to the skis.
Consider using a quick release fork mount to attach the front bracket and ski to the fork. This design was very effective and saved me from making an alternate attachment mechanism.
For the rear bracket use a 2x4 to span the distance of the rear dropouts. Drill a hole for the axle to slide through. Washers and nuts can be threaded on to secure the bracket to the dropouts.
Assemble your skibike and take it out for a test ride!