The First Step
The first thing new players should do is get familiar with the menus. Once familiar, begin by training your stats to at least 10 and battling John Doe in the home district. After you succeed you'll unlock your first restaurant.
Owning Your own restaurant.
Your first restaurant will have no theme specialization, which means all food here is equally viable. Put whichever recipes you have in your menu and begin selling -- or simply click the Auto button in the Menu screen, to let the game choose the best dishes for this restaurant.
John Doe should be hired by default, but you won't have any waiters yet. Restaurants without waiters have a speed penalty, so it is a good idea to always have at least one waiter in all restaurants. It's highly recommended that you turn on automatic staff hiring by going to the Info screen, then clicking the gear icon, then toggling Auto Hire Staff. If you opt to hire staff manually, make sure you have at least 1 waiter in each restaurant.
Your menu will be fine for now with whatever you put in it. The more dishes in a menu the slower each individual dish sells, but overall more dishes = more profit.
Pushing Forward and Fairies.
After getting your restaurant set up, you'll want to challenge Jane Doe. Her stats are higher than John's, so feel free to train a little longer to ensure victory. Once you beat Jane you'll be ready for your first retirement. When you retire, you start the game over as a pupil of your previous chef. You'll gain modifiers to your training speeds, research speeds, and fame based on previous stats. When you pupil for the first time you'll unlock a magic token which will allow you to buy a single pet.
The two most common starting pets are the Light Fairy and Fire Fairy. It is highly recommended to pick the Light Fairy as your first pet as it makes progressing much faster due to it increasing your pupil modifiers. Because Pupil modifiers help with almost all aspects of game-play the Light Fairy is generally useful in all situations. The Fire Fairy also gives you a modifier to all cooking battles which comes in very handy in late game play.
Pets can be used in two different ways: either as a mascot in a restaurant, which boosts income from that restaurant, or "meditating" (not assigned as a mascot). Unless you're desperate for income, you should let your pets meditate, because this lets them grow (gain levels, and thus gain higher multipliers).
Pets can be fed whenever their Satiation level is below 87.5%. Feeding them increases their Magic Growth (which makes them gain levels faster). After 8 "good" feedings (a dish with the randomly-selected Theme that the pet wants), you can receive a Magic Bag with maximum rewards. Always wait until 8 "good" feedings before claiming your bag.
You earn a cooking medal each time you win a cooking battle, except that you only get a medal for the first two areas the first time you beat them. Cooking medals allow you to purchase permanent upgrades -- see below. For now, just hold on to your medals.
You can also get 10 cooking medals per week by doing the "weekly quest" -- click the scroll icon above your portrait for details.
Research and Themes
The next areas will have higher research and differing themes. The exact themes and levels can be found in the areas page. Overall, you should begin progressing, unlocking more restaurants and winning more cooking battles. Quality Research helps the most in cooking battles, while Speed Research tends to help profit from restaurants, but both are useful.
Keep pushing and retire once you feel like your modifiers are high enough. It's common to wait until they are between 2 to 5 times your current modifiers in the beginning. Once you beat the Museum district you'll unlock challengers.
Challengers and Secrets
Challengers will appear every hour. The main determining factor in success is your Quality Research levels. The first challenger tier will require higher than 10 and is relatively easy. Challengers will match your highest Quality recipe and your stats (later challengers will have higher than your stats!).
Beating a challenger will earn you cooking medals, money and fame. The recipe used will gain a number of secrets depending on the level of the challenger: secrets = level + 1. Secrets act like permanent research levels for your recipes split between both speed and quality. Your main goal for now is just the cooking medals and income from winning.
Upgrades Upgrades Upgrades?
By now you'll have accumulated some cooking medals. What should you spend them on? Well, the short answer is everything. Overall you should focus on training and research speed, which you should only purchase in 30-medal (+100%) increments.
Then you should pick up a few levels of ingredient freshness and ingredient quality as they are cheap and useful for cooking battles and progression. Income should be your next major priority. Increasing the ingredients per recipe can be helpful, and eventually you must be able to create recipes with at least 5 ingredients (for curry). However, once you beat some areas you'll unlock recipes you can use in the meantime, so upgrading ingredients per recipe will take a lower priority.
Always keep at least one medal for battling a challenger, unless you're absolutely sure you can win a new area before the next challenger.
You have also probably noticed by now that you can buy upgrades for your areas, increasing their max population and median income. It's best not to spend money on those initially, but later on they will be very helpful. In any event, you might as well dump all your money into buildings when you're about to retire, since you will lose all your money anyway.
Once you beat the Office district, you'll unlock training upgrades. They function as a multiplier to your stats and can be very helpful in pushing areas and necessary for later areas. Once you unlock this feature you're fully equipped to continue climbing.
As you climb, continue to purchase permanent upgrades. After your initial upgrades, you can focus on getting ones such as max menu, more max ingredients, and ad duration. However, it is still recommended to focus on income upgrades first, followed by training and research. Your research speed will always be capped by your income, as researching costs money.
Area 30 and beyond
You beat area 30 -- congrats! You should unlock a second free magic token. It's highly recommended to get a Fire Fairy if you haven't got one yet. It'll be helpful in the trials to come. Now you should unlock challenges. The recommend challenge path is to complete 3-4 challengers challenges before tackling pupil's pupil challenges.
The reason for this is challengers challenges allow you to stay at area 30, and take your time upgrading recipes, using this time to grind more money and upgrade your areas. This can help you get a major edge in challenges and the game in general. The current recommend strategy is to upgrade a few (3-5) areas and use the profits from those to begin to upgrade the remainder to a specific base level. A good aiming point is around 50,000 population and $15,000 income for all areas. Your main areas of course can and should be upgraded much higher.
After completing your first 3-4 challengers challenges you can choose to either do some pupil's pupil challenges or try to push to 5 challengers challenge. There is a power spike at level 5 and using a research potion can help, assuming you have the income to cover the extra research costs.