To train construction you will need to buy planks ( yanille skilling shop ) and coins.
Since the path is long you might replace some of the planks in inventory with super energy points.
Here is a picture of the path to the estate agent.
How does the training work? It's simple! Just buy objects with suitable level and price - you get xp for buying.
A little bit more about construction: once you purchase a certain item - the corresponding object is added to your house. To enter your or your friend's house use yanille portal.
Also, as you know LUMBRIDGE ALTAR has been disabled for prayer training but now you are able to use own altars with the identical function. However altars that are almost same powerful as the dismantled one in lumbridge require over level 70 construction.
Houses also have thrones, teleporters and etc...
Of course you still do not understand - WHY THE HELL IS TRIP TO THE ESTATE AGENT SO LONG? Why can't I move it closer to the bank?
Before you start flooding that - please notice that high level construction object cost over 1 million. Those give A LOT OF XP. But who could be interested to buy high level objects and waste a lot of gold pieces if buying low level ones would be nearly the same speed. That's the reason - the distance will give huge advantage to those who pay money. It IS possible to get 99 construction for LESS THAN 2 HOURS. But the price is rather high.
If you still do not believe me, here are my calculations:
MINUTES - PRICE
32500 - 1.5m
16725 - 3m
10750 - 5m
6500 - 12m
3500 - 17m
3250 - 22m
2750 - 24m
2100 - 25m
1675 - 30m
1625 - 35m
1500 - 37m
1350 - 40M
1125 - 48m
1050- 51m
810 - 60m
800 - 61m
600 - 75m
400 - 125m
350 - 140m
325 - 150m
160 - 320m
150 - 335m
135 - 350m
105 - 390m
65 - 420m
60 - 430m
p.s. - for the ways requiring less than 600 minutes multiply on approximately 1.5 because you cannot purchase high level objects at low level.
Thank you for reading.