Hi peeps, can someone help me out? I want to make a Minotaur barbarian into an Aasimar at a certain point in the character's story arc. Is there a guide out there for how to do that? Can someone point me in the right direction?

By RAW, there's nothing that allows you to change races. You're going to have to work it out with your DM if you are allowed to, and how they want to do it, in terms of just switching from one to the other, or using a custom lineage as described in TCoE. If they allow it.

Thanks.

If you mean switching races completely then I'd ask your DM if you can seek out a Reincarnation spell (replacing the chance to turn into a tiefling for a chance to turn into a assimar) this will likely require a Druid and may also end up with you turning into something else entirely or you could ask your DM about the possibility of a little quest line that ahcieves your goal of reincarnating into an Aasmiar upon completion but thats upto them what it would entail.

Depending on the type of barbarian you went for there are a couple of primal paths that could lend themselves to a thematic reason for your transforming which might help your DM out, such as the Path of the Ancestral Guardian (if you chose your ancestral protectors to look like angelic/assimar like beings) or the Path of Zealot whereby if you die and get restored to life you come back as an assimar and it is seen as a privilege to be reincarnated.

If you're referring to becoming an Aasimar by adding a template to the Minotaur race, that is not possible by RAW. There might be some sort of applicable custom lineage via "rules" from Tasha's Big Bowl of Whatever Your DM Will Tolerate No Seriously Just Make Some Stuff Up and Say It's a Rule Now, but I generally avoid that particular publication. RAW Aasimar (and Tieflings) are explicitly planetouched humans, meaning they are humans with a sufficient degree of heritage traceable to a celestial (or fiendish) source to qualify them as a mechanically distinct race. Previous editions (at least 3.5 that I know of) include rules for templates that are literally extra stats you stack onto an existing character, but that system is absent in 5e. RAW there are no "Minotaur Aasimar," nor are there Orc-Aasimar, Dwarf-Aasimar, Gnome-Tieflings, etc. Some DMs may let you flavor an Aasimar/tiefling character as being from a non-human race and just use the normal racial stats poured into the cosmetic mould of said race, but that falls into the purview of "Ask Your DM." 

If you are the DM in this case, you could possibly just make up an improvised template and tack some extra things onto the character. You should beware of making the character overpowered compared to the rest of the party (and also when factoring encounters) if you're going to just give them all of the Aasimar racial traits on top of the pre-existing ones because that will give them twice the cool stuff as other PCs have in that regard. And yes, it will make a difference in one way or another and come up in game because that's what stats and abilities do. Templates back in 3.5 would almost always come with a level adjustment; a level 1 character with a template carrying a +3 level adjustment would be counted as a fourth level character for purposes of experience and encounter balance. Even if you eschew the Aasimar racial ability score bonuses, the addition of darkvision, Healing Hands, resistance to radiant and necrotic damage, plus whichever subrace ability is chosen is easily enough to balance out the extra abilities most classes get on a level up, possibly two. If I were going to do that I'd probably treat the "becoming an Aasimar"  as a level in a new class that grants those features, and no additional hit points, proficiency bonus, spells, or anything else. It might be something resembling balanced to a "good" level from most classes by sacrificing a hit die and a being a level behind for proficiency bonus purposes. Those are a lot of abilities compared to what any class typically gets on a level up.

How do you envision this happening? Not in a mechanical sense, just what you assume will happen to the character to trigger this switch? Result of a Wish or other spell? Cursed? Reversal of a curse? Weird sciency device? Divine intervention? It-just-happens-and-nobody-knows-why-or-how? Mechanics can follow from there, not the other way around.

Yeah, this definitely needs a bit more explanation... do you intend for the character to stop being a minotaur entirely and become a human-like Aasimar, or would you rather have them become a minotaur/Aasimar hybrid? And if going for the hybrid, what kind of combination are you hoping to accomplish?

I think it's not hard to envision.  We're talking about a race that is more "plane touched" than a true race after all.  Adventure spoiler,

 If I wanted such a "planetouched after char gen" phenomenon, I'd probably make a feat reflective of the Aasimar's non ASI features.  It's a BIG gift, so I'm not sure how I'd balance it in the game beyond that.  Maybe rely on the Draconic gifts in Fizbans as a balancing go-by.