I spent about an hour on google when I was aiming to marry her. Here is a basic outline :
1. Turn her dark, there is no romance option on light. ( Make her kill her master).
2. Go to Imperial Fleet and buy 63 Weapon gifts. Assuming you are aware how this works, if not let me know.
1 Lvl 1 Green Weapon Gift = 96 Affection to 2000, then 48 Aff to 4000. 63 Gifts = 12600 Credits.
3. Now from 4000 to 10000 affection option A - Buy/Crew Skill gifts lvl 3+ until 10K affection. Option B - Slower but cheaper select as evil as possible quest choices, ESC key useful for this.
4. She is dependant on your storyline quest progression, earliest you can marry her (9K affection to marry btw, 5K affection approx to start flirting) is at lvl 42. I finished Hoth missions then I was able to proceed.
Useful Tips :
Make sure to flirt as soon as the option comes available.
If your Vette affection is high, you will need to choose between them, choose Jaesa.
Not effective if levelling a Light Side Sith, as your Light options will diminish her affection gain through quests. ( Better option is Vette which you can marry at the end of chapter 2.)
EDIT : Forgot to mention basic guide to gifting Jaesa
Weapon/Luxury - Best highest possible affection
Courting - ONLY good when you romance her, useless before
All others are next to worthless.
For details, questions feel free to ask I will do my best to answer them.
Only way is the dark side. Lvl 12 Dark Side V Marauder Personal Achievement