By morning Casterly Rock seemed a small price to pay to be near her always. He gave his consent, and Cersei promised to do the rest.

How did Cersei aid in Aerys II naming Jaime to the Kingsguard?

We are told in AWOIAF (a little biased when it comes to extremely recent Lannisters):

In 281 AC, however, the aged Kingsguard knight Ser Harlan Grandison passed away in his sleep, and the uneasy accord between Aerys II and his Hand finally snapped, when His Grace chose to offer a white cloak to Lord Tywin's eldest son.

At five-and-ten, Ser Jaime Lannister was already a knight—an honor he had received from the hand of Ser Arthur Dayne, the Sword of the Morning, whom many considered to be the realm's most chivalrous warrior. Jaime's knighthood had been won during Ser Arthur's campaign against the outlaws known as the Kingswood Brotherhood, and none could doubt his prowess.

Ser Jaime was also Lord Tywin's heir, however, and carried all his hopes for the perpetuation of House Lannister, as his lordship's other son was the malformed dwarf, Tyrion. Moreover, the Hand had been in the midst of negotiating an advantageous marriage pact for Ser Jaime when the king informed him of his choice. At a stroke, King Aerys had deprived Lord Tywin of his chosen heir and made him look foolish and false.

Yet Grand Maester Pycelle tells us that when Aerys II announced Ser Jaime's appointment from the Iron Throne, his lordship went to one knee and thanked the king for the great honor shown to his house. Then, pleading illness, Lord Tywin asked the king's leave to retire as Hand. -TWOIAF, The Targaryen Kings: Aerys II

The marriage to Lysa was mentioned in world:

"I once hoped to marry your brother to Lysa Tully, but Aerys named Jaime to his Kingsguard before the arrangements were complete. -ASOS, Tyrion III

But prior to Jaime being named to the Kingsguard, he stopped at King's Landing and Cersei mentions:

You would not like the truth. He had joined the Kingsguard for love, of course.

Their father had summoned Cersei to court when she was twelve, hoping to make her a royal marriage. He refused every offer for her hand, preferring to keep her with him in the Tower of the Hand while she grew older and more womanly and ever more beautiful. No doubt he was waiting for Prince Viserys to mature, or perhaps for Rhaegar's wife to die in childbed. Elia of Dorne was never the healthiest of women.

Jaime, meantime, had spent four years as squire to Ser Sumner Crake-hall and earned his spurs against the Kingswood Brotherhood. But when he made a brief call at King's Landing on his way back to Casterly Rock, chiefly to see his sister, Cersei took him aside and whispered that Lord Tywin meant to marry him to Lysa Tully, had gone so far as to invite Lord Hoster to the city to discuss dower. But if Jaime took the white, he could be near her always. Old Ser Harlan Grandison had died in his sleep, as was only appropriate for one whose sigil was a sleeping lion. Aerys would want a young man to take his place, so why not a roaring lion in place of a sleepy one?

"Father will never consent," Jaime objected.

"The king won't ask him. And once it's done, Father can't object, not openly. Aerys had Ser Ilyn Payne's tongue torn out just for boasting that it was the Hand who truly ruled the Seven Kingdoms. The captain of the Hand's guard, and yet Father dared not try and stop it! He won't stop this, either."

"But," Jaime said, "there's Casterly Rock . . ."

"Is it a rock you want? Or me?"

He remembered that night as if it were yesterday. They spent it in an old inn on Eel Alley, well away from watchful eyes. Cersei had come to him dressed as a simple serving wench, which somehow excited him all the more. Jaime had never seen her more passionate. Every time he went to sleep, she woke him again. By morning Casterly Rock seemed a small price to pay to be near her always. He gave his consent, and Cersei promised to do the rest.

A moon's turn later, a royal raven arrived at Casterly Rock to inform him that he had been chosen for the Kingsguard. He was commanded to present himself to the king during the great tourney at Harrenhal to say his vows and don his cloak -ASOS, Jaime II

Potential Options

Note: Current Cersei is basically incompetent, but that is largely due to her alcoholism and paranoia. Its possible that younger Cersei was a little more controlled:

His sister was not without a certain low cunning, but her pride blinded her. She would see the insult in this, not the opportunity.

So what happened? A few options (if we operate under the assumption that Cersei was at least involved):

Cersei seduced Aerys

Aerys was known to have numerous mistresses and was infatuated with Cersei's mother. That said he supposedly stopped seeing mistresses after his new son Jaehaerys died.

If so she may have ruined her chance at marrying Rhaegar:

Her laughter died at tourney's end. There had been no final feast, no toasts to celebrate her betrothal to Prince Rhaegar. Only cold silences and chilly looks between the king and her father. Later, when Aerys and his son and all his gallant knights had departed for King's Landing, the girl had gone to her aunt in tears, not understanding. "Your father proposed the match," Lady Genna told her, "but Aerys refused to hear of it. 'You are my most able servant, Tywin,' the king said, 'but a man does not marry his heir to his servant's daughter.' Dry those tears, little one. Have you ever seen a lion weep? Your father will find another man for you, a better man than Rhaegar." -AFFC, Cersei V

Cersei alerted Aerys about Tywin's plans w/Jaime & Lysa

Its possible that Cersei alerted Aerys, but how would a 15 year old girl know something that the King doesn't (Varys arrived in 278 AC).

These are the type of things that Varys knows:

Lord Tywin meant to marry him to Lysa Tully, had gone so far as to invite Lord Hoster to the city to discuss dower.

and:

Old Sumner Crakehall sent me to deliver a message, one he swore could not be entrusted to a raven. Lord Hoster kept me for a fortnight whilst mulling his reply, and sat me beside his daughter Lysa at every meal."

"Small wonder you took the white. I'd have done the same." -AFFC, Jaime V

Although its possible Varys could have withheld the information.

Cersei had someone else give the idea to Aerys

We know that there were numerous in King's Landing who were not fans of House Lannister:

Nor did His Grace agree to appoint Lord Tywin's son Jaime as squire to Prince Rhaegar; that honor he granted instead to the sons of several of his own favorites, men known to be no friends of House Lannister or the Hand. TWOIAF, The Targaryen Kings: Aerys II

- House Lonmouth (Richard)

- House Mooton (Myles)

If interested: Small Detail about Jaime Lannister and the Knight of Skulls and Kisses

Other potential characters she may have spoken to (however unlikely) include Rhaegar, Rhaella, Hoster Tully, etc.)

Cersei wasn't actually involved

Needs to be at least mentioned. Maybe she planned to do something but it ended up happening anyway.

We don't have enough information to know the answer to this question. We also get POVs from both Jaime/Cersei and it doesn't really come up again. It could easily never be brought up again.

TLDR: Cersei promised to do the rest (in order to help Jaime get on the kingsguard). Using this logic, I looked at a few potential ways in which she could have aided.