The basic formula is simple: kill units, gather corpses, return to Orifice/Colony/Hive, progenerate Harvesters, gather lumber.
You can gather corpses from any organic unit you kill (does not include rock golems or summons) using your Terra. It has 8 slots to hold units, so of course the most efficient units to pick up are those that only take one slot. You should always have at least one Terra with your army during any battle, even if you lose you could escape with some corpses.
If you have more of an eye for turtling you can do this to some extent because killing your own units next to your hall will also generate Harvesters - i.e. produce Beasts and then order them to kill each other. This is however much slower than creeping and leaves your base undefended. The Seed are very weak early game and usually need a three to one ratio to win a fight (three Beasts to one Footman).
Once you get a good amount of Harvesters you'll want to pay attention to what they are doing. You will go through forests at a fast rate and you want to make use of Nourish to sustain your perimeter. You can also use this process to construct buildings within the forests and then encase them in trees for protection.
You do have a second option though, and it is much more risky. Siphon allocates you bile (lumber) from any organic unit you kill. Some units have higher values such as Dragons with 150 and others aren't worth much like Footmen with 50. This means that if you are an extremely aggressive player it is possible to not have to harvest lumber beyond the first few minutes. This is a risky tactic and of course the smarter path to take is a mix of the two methods, but obtaining Harvesters is a process.
The benefit in this is of course that you don't need gold and thus you can survive anywhere there are trees. On that note you will notice several sizes of trees around the map in addition to the standard trees that have 50 lumber: Old have 100, and Ancient have 150.
Whatever you choose you need to be quick about it as the Seed fall apart when there is an interruption of lumber intake.