Gym Battles
You cant do gym battles until you reach level 5. Once you are level 5, you just need to get in range of the gym like a pokestop.
The best way to fight is to simply tap the screen as fast as possible. Maybe this changes as people put harder pokemons defending, but i had the most success with ignoring the type of pokemon and just tap that screen as fast as possible.
I made the mistake in my first gym battle thinking it was turn based, its not, just attack!

Sometimes you will take the enemy pokemon down to a slither of health and it does seem to want to get rid of the rest. Again, the best success i've had with this is to just keep tapping the screen (ignore the fact your pokemon are dying, just tap that screen)
The pokemon that is displayed as the owner of the gym is not the most powerful pokemon in the gym. Its literally the first pokemon that was put into the gym when it was taken over. So just be aware.
Every 20 hours, you can goto the shop and click the shield up the top right that will give you coins and dust based on how many pokemn you have in gyms. So its good to go get all your local gyms and then do the shop.
Sometimes you have to do multiple battles to take over a gym, after each victory, just click and fight the gym again until it goes neutral.

Catching Pokemon
In the bottom right is a "nearby" list of pokemon, if you click that button, the less the number of foot prints, the closer the pokemon is. If any of them have no footprints, click on them from that list and they will appear.
Going near "rustling" grass is no guarantee to spawn a wild pokemon - but often i would run into multiple if i walked around that area for a little bit.
I found if i just left the pokemon app open while next to my bed, or just turn it on every now and then, there would be a wild pokemon spawned.
You need to score a direct hit on the pokemon with your pokeball to catch them - i've found that after a while, you pretty much 1 shot 80% of the pokemons once you get your eye in. Sometimes the pokemon will "escape" the capture and either run away (bad luck) or continue to fight and you can try catch again.
It costs you 1 pokeball per throw, i havent been close to running out but i can imagine if you dont constantly get pokemon in 1 or 2 throws, perhaps it could happen.

Healing your pokemon

Pokemon do not heal naturally over time , which is a shame, but they also only take damage when you do a Gym battle. But below are the ways i have found to heal them.
There are 3 ways to heal your pokemon:
Using a heal (purple) potion from your items
Powering up your pokemon (Will restore 1 hp each time - yay!)
Evolving your pokemon restores it to the full health of the next level pokemon

Reviving your pokemon
There are 2 ways i've found to revive your pokemon
Using the revive (yellow) potion from your items - restores pokemon to half health
Evolving your pokemon - revives and gives them full health

Getting Healing and Reviving potions
You get them from the pokestops, but i found i only started to get them once i had dead and injured pokemon in my inventory. Before that, i rarely got them. So i would recommend not just sending them away once dead as it may impact the drop rate of these items.
You also get some when you level up at certain levels, but that takes time obviously.

What to do with dead pokemon?
Your options once a pokemon has been killed is to either turn them into 1 candy of their type, or heal / revive / evolve them if you want to continue to use them.
To turn them into 1 candy, click on the pokeball -> pokemon -> select the pokemon you want to convert -> scroll down and hit the "transfer" button. That will convert them into 1 candy.

What does CP of a pokemon mean
CP is the combat power of the pokemon, the higher the CP , the stronger the pokemon.
You can increase CP by Powering Up your pokemon (it can only go as far as the semicircle line above your pokemon - once its full white, thats it).
You can also increase your CP by evolving the pokemon - which converts it into the next evolution of the pokemon which comes with increased CP

Eggs
Once you have picked up an egg, make sure you have it in the incubator!! Do this by clicking the pokeball -> click "pokemon" -> up the top right, select the "Egg" list -> click on an egg, and assign to the incubator.
I'm unsure if an egg that takes longer to krack is better or worse. I have 3 distances so far, 10km, 5km and 2km.
I also found an additional incubator in a pokestop so i can incubate 2 eggs at a time (for 3 attempts before the picked up incubator breaks)

Driving
Driving under 20 kmph seemed to count as walking - kracked an egg doing some loops in the car - unsure what the max speed is that it counts, but my train ride didnt count at all So there is a max speed.


Combat

Combat is real time, its not turn based.
You can do 4 things in combat:

Tab the screen = Attack
Swipe left/right = Dodge
Tap and Hold = Special Move (You require 1 bar of blue built up which is done by attacking)
Swap the current pokemon (so far, this just makes you take way too much damage as combat is real time - just tap the screen for now - may change once pokemon are stronger)

My Bags Are Full, What should i do?
You have to either buy more bag space or delete some items. For the team, i pressed the "bin" icon on my pokeballs and hoped that it didn't delete them all - it didn't, it asked me how many i wanted to delete so i could throw away 30.
If your bags are full and you visit a pokestop, you wont get ANY items but you will still get the XP

The Incense Item
Using Incense will make it active for 30 mins from that time - even if you are offline. I used an Incense, got booted from the server, and when i finally got back in, it was down to 15 mins.
I saw a slight increase in number of wild pokemons that popped up, but i was expecting more - hard to tell how much it does.

How to get Candy?
There are 2 ways to get candy:
When you catch a pokemon, you get 3 candy of the pokemons type
You can send your pokemon to the professor to get 1 candy (but you lose the pokemon permanantly obviously)

Should i evolve X Pokemon?
Evolving takes a different amount of candy depending on the type of pokemon. I'm a hoarder in games so i have a hard time spending my currency, but i would only recommend evolving a fairly strong pokemon. I think its better to hold onto the candy until you have a decent pokemon before evolving.
I would also not spend candy on powerup's until the pokemon is max "evolution" as it just delays how quick you can build up your pokemon. I didn't see an increase in the "Power Up" cost after evolving so i dont think you need to consider powering up before evolving.

Battery Saving Mode
Recommend you turn this on , click the pokeball -> click top right settings -> then activate the battery saver mode. It means while the phone is upside down, the screen will turn off but everything else still runs. Just hold onto the phone with earphones in and it will vibrate when a wild pokemon is near or make a noise when you get in range of a pokestop.