In those times, chances are they moved the build site to the trees, and made sure the trees were close to the water (with more forest and a much smaller population, such trees could probably be found fairly easily)
“Timber was used green – in other words, shortly after felling. This is different to more modern practice, where the timber is "seasoned" – left to dry for several years. Green wood is easier to work, and more flexible, which can help with some of the more complex shapes found in Viking boats. Wood can be kept "green" for several years by keeping it immersed in water – a stem (or stern) of a Viking style boat was found on the island of Eig in what, a thousand years ago, had been a lake. As it had never been used – there were no indications of rivet holes – it was probably made up when the boat-builder had got a spare piece of suitable timber, and he was waiting for a similar bit for the stern (or stem) which never arrived.
It is also possible to steam green wood without complex equipment like the steam boxes used today. Simply by heating a plank over a fire, the moisture inside the wood heats up and causes the fibres to loosen. This means that – for a few minutes – it can be twisted into shape with less danger of it splitting and breaking. It is highly likely that this was done during Viking times – we know the technique was used to make "expanded" log boats, for example.”
Also, they didn’t dry the wood. https://regia.org/research/ships/Ships1.htm:
“Timber was used green – in other words, shortly after felling. This is different to more modern practice, where the timber is "seasoned" – left to dry for several years. Green wood is easier to work, and more flexible, which can help with some of the more complex shapes found in Viking boats. Wood can be kept "green" for several years by keeping it immersed in water – a stem (or stern) of a Viking style boat was found on the island of Eig in what, a thousand years ago, had been a lake. As it had never been used – there were no indications of rivet holes – it was probably made up when the boat-builder had got a spare piece of suitable timber, and he was waiting for a similar bit for the stern (or stem) which never arrived.
It is also possible to steam green wood without complex equipment like the steam boxes used today. Simply by heating a plank over a fire, the moisture inside the wood heats up and causes the fibres to loosen. This means that – for a few minutes – it can be twisted into shape with less danger of it splitting and breaking. It is highly likely that this was done during Viking times – we know the technique was used to make "expanded" log boats, for example.”