Well, it could be a fan - made story where Sakura, from the Naruto series, plays a crucial role in saving Obito. Maybe it involves her using her medical ninjutsu skills to heal him from some critical injury or her strong will to bring him back from the dark side he was on.
One possible plot could be that Obito arrives just in time to save Rin from being captured by enemy ninjas. He uses his Sharingan abilities to outwit the enemies and then escapes with Rin. Maybe he has to fight through a horde of strong opponents, but his determination to save Rin gives him the strength to persevere.
One common theme is redemption. Since Obito has made many mistakes in the original Naruto story, in time travel fics, he often gets a chance to right his wrongs through his interactions with Minato. Another theme is the alteration of fate. Time travel allows for the possibility of changing the pre - determined course of events in the Naruto universe.
In a fanfiction where Team Minato meets future Obito, it could be a very emotional encounter. Minato might be shocked to see how Obito has changed. Obito, having experienced so much in the future, could bring warnings about future disasters. For example, he might warn about the upcoming threats to Konoha. Team Minato would have to grapple with the knowledge that Obito is no longer the person they once knew.
In some fanfictions, Naruto saves Obito by first understanding the root of Obito's pain. Obito was driven to his actions because of the loss of Rin and his disillusionment with the ninja world. Naruto, having experienced his own share of losses, is able to empathize. He then uses his positive influence and unwavering belief in the goodness of people. For instance, he might show Obito the new, more united ninja world that he has been working towards. This gives Obito hope and makes him realize that there is still a chance for a better future, and thus he is saved.
A common plot element is Obito's change of heart. Usually, he has been a villain or on the wrong side, but then he realizes Naruto's importance and decides to save him. Another element is the danger Naruto is in, like from a powerful enemy or a dangerous jutsu.
Another idea is that Naruto's strong will and determination somehow reach Minato in the past. Minato, inspired by this unseen force which is actually Naruto from the future, finds the strength within himself to overcome a seemingly impossible situation. This could be during the Nine - Tails attack on Konoha, where Naruto's spirit gives Minato the idea to seal the Nine - Tails in a different way that doesn't cost him his life.
One great 'Minato Saves Naruto' fanfiction is 'A Father's Promise'. In it, Minato manages to break free from the death seal's constraints just in time to save Naruto from a powerful enemy. Another one could be 'Minato's Return', where Minato is brought back to life through some powerful jutsu and he immediately focuses on protecting Naruto. And then there's 'Saving His Son', which shows a very emotional journey of Minato coming back to save Naruto from a life - threatening situation.
The village of Konoha would also be affected. With Minato still alive, he could continue to lead the village and make different decisions. This might change the relationships between Konoha and other villages. For example, there could be more peaceful alliances as Minato is known for his diplomatic skills. Also, Kushina being alive would mean that the Uzumaki clan might have a stronger presence in the village, which could lead to new jutsu developments and a different power balance within Konoha.
There's a fanfic called 'Obito's New Path'. In it, Obito has a change of heart after seeing Naruto's unwavering belief in friendship. He decides to save Naruto from a dangerous plot by some rogue ninja. The story delves into Obito's internal struggle as he tries to make up for his past mistakes while saving Naruto.