Couple of things as to form... This assuming you'll be on a roadster. Move back on the saddle a bit to allow more leg extension, and sit up and use the top-of-the-bar hand position. This will allow better chest expansion and ease breathing to a small degree.
If you have clipless pedals, you'll find they assist climbing to a fair degree. You can "pull through" the bottom of the pedal stroke; the motion has been described as "wiping mud off your shoes".
Standing can be a help, but tends to work best for smaller riders. The pros you see "dancing on the pedals" tend to be the littler guys; big riders are generally sitting and slogging it out in an optimal gear.
If you do stand, you'll find shifting UP a couple of gears will work better.