Here's a few tips that may help youn while your training your contruction skill.

1. The most efficient way of training contruction I found is to build and demolish and rebuild oak larders, for ease of use it makes sense to have a 2^nd "training kitchen" built into your house to help this. What makes this so effective is oak planks are cheap and fast to aquire.

2. To get your oak planks fast, simply carry your GP, Varrock teleports and a hatchet, run up to the plank converter guy, chop oak logs at the spot near him, have him convert them to planks, teleport to varrock and use the east bank to bank your load of oak planks, then simply run up and repeat as much as neccessary.