My first companion is ember and I don't understand what rapport is or how to increase it to be friends with ember. I'm new to the companion system and need some help of how it works.
If you want to know their likes/dislikes more naturally you can talk to them and they would point you slightly to potential things that increase or decrease their rapport.
A number of things (detailed I'm sure in the link above) can raise or lower Ember's rapport by small amounts. The big one to remember is that turning in a Mages Guild daily gets you a very big (+125 points) rapport boost, so try to do one of those each day while leveling up her rapport and you won't have to worry much about losing one point fishing or gaining one point when you enter an outlaw refuge or harvest a runestone.
To level their guild skills (Mage, Fighter, Undaunted), do the dailies for those guilds.
To level their weapon skill, equip them with the appropriate weapon.
To level their armor, they need to wear at least 5 pieces of the weight you want them to level.
To level their character skills and overall level, kill stuff. They share some of the XP you get when you kill things. The more XP from killing things you get, the faster they level up. So things like XP scrolls that boost your XP will help level them faster.
To add to AcadianPaladin,, Ember also love doing Thief guild heist but unless experienced or having stealth gear they are harder but it does not matter if you fail.
Now the only thing Ember hate is getting caught by guards stealing or trespassing.
She is easy going and works great healing you or helping kill enemies.
Then leveled up you can swap skills around so she only heal on an world boss or group challenge.
Its also other companions Isobel and Bastian can be decent tanks, Sharp is also funny.
I am pretty sure that companions level up faster if they have higher rapport. So make the big daily rapport increases (Mages Guild, High Isle Delve, Thieves Guild) first thing you do each day. Then any XP killing you do rest of day will level Ember just a little bit faster. And she'll occasionally pop up a quest marker over her head. These are her personal story quests that she shares along the way. I think there are 3 or 4 and they give a huge amount of rapport. So do them ASAP to, again, help her level up a little faster.
Aside from looking at lists of a specific companion's likes and dislikes, you should notice a rapport indicator pop up in the bottom right corner of the screen as you do things while that companion is summoned, down in the same area where you see things like gold, experience, inspiration, or items that you've just looted or been awarded.
There are indicators for a rapport increase, and other indicators for a rapport decrease. If you start seeing those pop up, try to make a mental note of what the companion likes or dislikes, as well as which activities elicit a strong like or dislike versus a milder like or dislike. Note that certain likes are going to be a once-a-day thing, whereas others can be repeated throughout the day.
Also, note any skill lines the companion has which are associated with specific faction guilds, such as Fighters Guild, Mages Guild, Undaunted, etc. The companion's levels in those skill lines will be increased by completing daily repeatable quests for those factions while the companion is summoned-- meaning when you turn the quest in and collect the reward, so be sure you don't dismiss the companion before you turn in those quests.