Unlocked after completing the main story of the DLC, this weed-growing simulation has a lot of moving parts.
The basic structure is this- there are five ranks of Herbalism you can acquire. At the start of each rank, MJ will send you to secure samples of a particular strain of weed (the first strain, Ditch Weed, is found right in the room, but later strains will need to be collected from randomly assigned locations around the city).
You then need to sell enough weed to earn your next rank, at which point you'll talk to MJ again, and he'll send you after the next strain, and the process repeats.
The main benefit to each rank is that it makes more upgrades available to you. These upgrades allow you to grow more/better weed, which allows you to sell it for more, which allows you to reach the next rank faster, etc. Reach Rank five and you'll get an achievement unlock, and access to MJ's van (Note that, on release, the decal mapping on the van is a little buggy).
The main drag on the process is that is usually takes at least day of game time to grow a batch of weed to the point where it can be harvested (which is phenomenally fast in one sense, but agonizingly slow in a more relevant one). Even using the Fertilizer upgrade only cuts down this time marginally. You can use this waiting period to run other missions (the three steal-things-from-the-Bayou-for-your-Underbosses missions remain evergreen), or just park Lincoln outside somewhere and walk away from your computer for about an hour. You can keep tabs on how complete the crop is by mousing over Laveau's compound on your map.
In terms of growing the most lucrative crop, you should always grow your own hybrid strains. The game doesn't quite make this clear, but way strains work is you hybridize your current strain with a new seed, which adds a given bonus (faster growing time, higher THC content, etc).
Once you've grown at least one batch of it, you can go back to the lab to re-hybridize the strain you just made, adding another seed for another bonus. All these bonuses stack, so by the time you reach Rank 5, you should have no trouble selling your batches for well over $10,000 (as required for the That Good Connect achievement).