Introduction
Cable is known for comboing into his extremely damaging Air Hyper Viper Beam (AHVB). Learn to wield AHVB, and utilize it well.
The biggest tip for all combos that go into AHVB right from super jump is to do a Tiger Knee motion. Start with 
, then roll the stick to 
. Then delay a tiny bit before pressing the buttons at once. This will give you a super jump input, followed by the input for the super. This is the main way to combo into AHVB, and the fastest way to get it off the ground.
Bread and Butter Combos
Cr. 
> Cr. 
> St. 
XX 
+
Cr. > Cr. > St. XX + 
or 
Leaves you minus and punishable on hit. Be careful when using this one.
Cr. > Cr. > St. x 4 XX 
+ 
XX Air +
Kara cancel the Psimitar into AHVB.
Cr. > Cr. > St. XX Super Jump XX Air +
Tiger Knee the super.
Air + , Air + , Air +
Tip for this combo, Tiger Knee the first one, and aim down. Tiger Knee the second one and aim either straight towards or down, depending on height. Last, Normal Jump and do the motion in the air. You have WAY more time than you think you do with this combo. Take it real easy and just make sure you hit the directions.
Ground to Air Combo
Cr. > St. 
> Super Jump > SJ. > SJ. > SJ.
Most consistent air combo. This isn't incredibly important for Cable, though.
Corner Combos
Most of Cable's regular B&Bs work anywhere, including the corner.
Assist Specific Combos
St. + call Sentinel drones > x 2 XX Electrap
This is a very good trap combo. On block, Tiger Knee a Viper Beam aimed down. On hit, Tiger Knee AHVB. Watch what your opponent does after this trap as well. If they rush you often, start calling your anti-air assist after the Viper Beam on the ground.
Style Combos
Don't do these unless you want to lose friends. And if you do, go nuts.
Cr. XX + , 
+
This leaves you with absolutely nothing afterward, you spent an entire bar to get this, and it's escapable with a roll, but hey, you landed one of the worst moves Cable has. Good job.
Corner (J. , D. St. XX 
+ ) x n
An infinite combo on standing Sentinel only. Not incredibly practical, but hey, it exists.