There are a few general important parts of EOC combat
1. Building adrenaline
-Every combat style has a basic ability with a 3 second cooldown. This can be used every other hit in order to build and keep adrenaline up effectively. Having adrenaline is important because it allows you to use more powerful attacks. at 50% adrenaline, threshold abilities unlock, and at only at 100% can ultimates be used
2. Prioritizing abilities
-Instead of spamming whichever ability is available, you must know which abilities are your strongest and should be used first, and which are weaker and should be used as a last resort. You should never be wasting time with autoattacks
3. Focus
-Although it is difficult to get used to, you must practice keeping an eye on your hp and prayer levels so you do not run out while watching ability cooldowns. A couple methods of doing this is to glance at it every once in a while, or you can memorize ability combos ahead of time. For practice with this, I suggest 'The Brink of Extinction' quest, or if that is finished, the Fight Cauldron minigame. They force you to watch the floor tiles, your enemies, and yourself to survive, it is very good practice.
Melee:
Twohanded Melee:
I recommend 2h melee for nearly all melee situations, the extra power is very helpful and it gives many multitarget options that are very useful in slayer, dungeoneering, and many other areas of the game.
This picture shows my current setup, it is designed to build adrenaline effectively and use it on powerful thresholds, rather than using ultimates.

#1 is the most basic ability and #3 has only a 5 second cooldown, 4 is a stun (may replace with backhand), and 5 is the most powerful basic ability. 6 is a bleed effect, and 7 is a combo attack, so you must remember not to interrupt it if you want full damage. #8 attacks surrounding enemies and can lower their defence, #9 is a stronger version with no special effect, and #0 only attacks enemies stacked together on the same space, not the area surrounding you. The last 2 are free for anything you may need, if you want to put food or quickprayers or defensive abilities there is up to you.
Please note: These are only basic descriptions, I highly suggest you read the in-game descriptions of all abilities for more details
A good way to build adrenaline to threshold level with this setup is 1,2,1,5,1,3
If you prefer using ultimate abilities, this can be rearranged to extend the combo: 2,1,3,1,5,1,3,1,2,1,3,1,4
Feel free to practice the combos at the lumbridge combat academy dummies to build the habit of using them.