Operating a charcoal hearth is fairly easy. Describing the procedure in a fully mechanical, scriptable way is extremely hard.
High heat is the key to charcoal happiness. When the heat bar is nearly full your progress bar will absolutely fly up. My best time for a batch is just barely over four teppyminutes on a charcoal oven, a rate of 25 cc/min. Unfortunately high heat gives your charcoal the nasty habit of bursting into flames. It's very difficult to get any sort of fine-grained control over oxygen, so maintaining a high heat level without spiking the danger bar is nearly impossible. You might get lucky for a minute or even two but eventually it will get away from you.
Heat also has a nasty habit of barely creeping up for several ticks, followed by a nasty spike. It almost reminds me of heat spikes on a glaziers bench; I wouldn't be surprised if the code is similar. If that's the case then good frigging luck ever writing a macro. Not only do you not get to see exact numbers for wood and heat, you also have the oxygen bar to deal with, AND there seems to be some extra randomizing each time you start the hearth.
The less fatalistic theory is that there are sweet spots at which wood and oxygen levels correspond for maximum and minimum heat generation. Finding these is... challenging at best. The research continues.
By all means use the 24 hours of free play time on your trial account, but when you want to truly get involved you have to pay. Many resources aren't available to trial players and most other citizens of Egypt won't take you seriously until you cowboy up the money like they did.
Lots of free stuff is available from Schools and Universities. At the very least, every new player should learn all of the free techs and get all of their free veggie seeds from the Universities of Worship (which are only available to paid accounts). Use the Research map to see where techs are available and the Chariot Stops map to plan out your route. This trip will probably take a few hours but you will get an interesting tour of Egypt.
While you're out walking keep an eye out for chests of free Flax seeds. The link describes several types and lists a few giveaway locations. I prefer "Golden Age" because it doesn't require watering. You only need a couple of seeds to get all the flax you could want.
Finding a good camp site is important but not difficult. You will probably see several good spots during your Egypt-wide tour of the Universities. Try to find a place with room to grow that doesn't crowd your neighbors. A good camp site needs easy and plentiful access to the following resources:
Almost every useful thing you can build must be built inside of a Compound. In short, you need 100 wood to learn the Compound Construction skill, then 100 boards and 200 bricks to build the initial structure. I suggest the "Gem Facets" style because it's slightly larger and perfectly square. Once you build your compound, immediately click on it and select "Utility... > Install a cornerstone" (this will prevent your compound from decaying).
This next step is important: Edit the blueprints of your compound and change all walls to the "plain" or "extruded" type, change all wall textures to "brick", and change the trim pattern to "stripe". This will require you to toss in some more bricks but it allows you to expand your compound later on using only bricks, straw, and flax. Other compound components require more expensive resources like Slate, Cut Stone, or Marble.
You might want to make some clay jugs to grow veggies. You might come across some iron and want to forge nails. Unfortunately the buildings that do these things are not easy for new players to make themselves. Eventually you will be able to make or trade for all of the parts you need, but to get started you can take advantage of one of the Public Facilities available throughout Egypt.
At this point you are nearing the end of what you can easily do on your own. The key to success in Egypt is being able to trade for the things that you need. Even as a newbie there are things you can produce that people will want to trade you for:
Trading with people near you is a good thing but if you're having trouble be sure to check out The Goods. The Goods is an excellent way for new players to get hooked up with just about anything they need.