How would you go about playing or implementing a tiny pc race, what problems would it bring up rule wise that you can think of?

I’m thinking about reach, in that if every 5ft square would be quatered as a tiny race, does that mean you need to be in the right quater to hit someone?

Every single thing about the Combat system is affected.  I am aware that it's in Unearthed Arcana right now being tested.  I am against it and will never allow it in my games.

The three pillars the game stands on are Combat, Exploration, and Social.  This isn't the forum for Social since there aren't any rules that should apply.  Combat is definitely affected, and Exploration so far as the few rules that apply to it go, is also affected.  I don't think after-battle healing is an issue, nor any kind of spell casting out of combat. 

Quote from Cheeky_Hamster >>

How would you go about playing or implementing a tiny pc race, what problems would it bring up rule wise that you can think of?

I’m thinking about reach, in that if every 5ft square would be quatered as a tiny race, does that mean you need to be in the right quater to hit someone?

It's not any different for PCs vs NPCs, and we've been playing with tiny NPCs this entire time.  Also tiny PCs - Enlarge/Reduce has enabled tiny gnomes, halflings, etc since 5E dropped.  You can certainly ask on here for clarity about the rules for handling a tiny creature, but a permanently tiny PC doesn't introduce any new rules headaches.

Quote from Lyxen >>

And what happens when you cast Enlarge/Reduce on a Tiny PC ? :p

On the one hand, I agree with you, it shouldn't be too bad, if your PCs behave. But considering the fauna on these forums, there is a lot of abuse and I can guarantee that someone will find a way to make this OP, probably in a very silly way.

The truth is that the system does not work really well already for small creatures. It's already a problem that they have the same space as medium ones (which means that you cannot squeeze a medium creature, for example) and that their weapons are not dimensioned smaller, with smaller damage, and that they are not physically weaker. 3e accounted for all that, even though it became really complex to manage, but 5e does not, for simplicity sake. But I personally would find it ridiculous to have a pixie with 20 str and wielding a 1d8 longsword made for a human for example.

Weapon dimensions do matter, but the rule is buried.  Worse, most size change mechanics disobey the weapon dimension rules, which can be hand-waved with magic, but it means knowledge of them is less likely to be well-known.  Also, the rules for scaling a weapon down don't exist, causing genuine problems like how a Quickling behaves absolutely nothing like a Sprite (the Quickling can't be wielding a "standard" dagger sized for Small/Medium PCs - it would be at disadvantage to attack, per DMG p278).

The rules for large+ weapons are buried in the DMG on page 278.  The rules for tiny weapons have to be constructed from studying the Monster Manual and reductively applying the DMG rules backwards, and you have to accept that monster statblocks are generally error-prone and never get errata, so your source material is suspect and it's within reason for a rule you come up with to only match some statblocks.

It comes down to this:

1. For size purposes, small = medium, so the different size categories are Tiny, Small/Medium, Large, Huge, Gargantuan. 
2. Each time you go meaningfully go up a category, a weapon's base damage should increment by one copy of itself.  Hence, 2d6 -> 4d6 -> 6d6 -> 8d6 for a greatsword of Small/Medium, Large, Huge, and Gargantuan sizes.
3. The only Tiny weapon-wielders in the game are the Sprite, the Quickling, and a named NPC named Traxigor, but let's ignore Traxigor, he's very special and shouldn't set precedent.  Neither the Quickling nor the Sprite make any sense, to be honest - Quicklings appear to be wielding a Small/Medium dagger with an inexplicable ability to not roll to hit with disadvantage, while Sprites have d1 Shortbows, as if their +4 Dex does nothing.  However, if we look at other Tiny creatures, a flat 1 damage is how their natural weapons generally work, regardless of dexterity - for example, both owls and poisonous snakes deal a flat 1 damage, ignoring their stat modifier.  This suggests Sprites are obeying the rules, and they work like the size+ ones backwards with a minimum damage of 1, resulting in all Tiny weapons dealing 1 damage of the appropriate type, regardless of weapon stats, and ignoring stat modifiers.
   1. Special mention:  Sprite longswords are an especially egregious rules violation, as there's no plausible way the things could have +2 to hit.  If ever you needed a reason to believe statblocks are error-prone, Sprite longswords are a quintessential example.

So that seems to be the two ways to let a Tiny creature wield a weapon without magic shenanigans - either it deals a flat 1 damage with no modifiers, or it deals "normal" damage and is at disadvantage.  Neither rule is great and both have shabby interactions with the Heavy keyword, but there it is.  If you want to homebrew a fix, it's actually very easy, because you can just halve the base damage, instead of cutting to a flat 1.  You'll cause some weapons to functionally gain damage when you coerce them to valid dice, but not in a significant way.

1. 2d6 -> 1d6
2. 1d12 -> 1d6
3. 1d10 -> 1d5
4. 1d8 -> 1d4
5. 1d6 -> 1d3
6. 1d4 - > 1d2
7. 1 -> 0 (tiny blowguns and punches don't hurt)

1d5, 1d3, and 1d2 are easily accomplished by rolling 1d10, 1d6, and 1d4 respectively, dividing the result by 2, and rounding up.

I played a homebrew pixie race in a campaign for quite a while, the race was tiny in size, but one of the traits was allowing for easier combat considering I still take a 5ft by 5ft square to combat and have normal reach, but could move through other creatures space that are larger than me without penalty.

But despite those simplifications, many problems came up during the game, if the items are scaled to my size, the weight too right? how does it scale exactly, especially as a tiny PC I had a much smaller carrying capacity. and ddb ain't really made for managing anything under 1 lb. Also yes, despite the simplification making It easier mechanically, haven't a pixie paladin wielding a two-handed mace to smack enemies was funny, but probably not the best representation of how a tiny char would fight. Overall, the system ain't designed for that at all, and i don't think it can work, at least not without a lot of work beforehand.

Also, been tiny is often quite overpowered when it comes to exploration, in a medieval setting, you do not imagine how many cracks, etc.. are big enough for a pixie to fit and sneak into places, or how easy it is to find a spot to hide (like a friend's pouch).