Tiefling tails look pretty flexible, but they probably don’t have much fine control over them

The books published so far (for 5e, at least) seem pretty thin on description of tieflings in the detail you want. By searching, the most I could find that referenced the tiefling’s tail is the default description given in the Player’s Handbook (pg 42):

They have thick tails, four to tive feet long, which lash or coil around their legs when they get upset or nervous.

And this part of the Variant Tiefling option in the Sword Coast Adventurer’s Guide (page 118):

Your tiefling might not look like other tieflings. Rather than having the physical characteristics described in the Player’s Handbook, choose 1d4 + 1 of the following features: … a forked tail…

And there’s also the official art. With those depictions in mind, here’s my take on the tiefling’s tail:
Flexibility

The official art of tieflings from the manuals gives them quite chunky tails indeed – the character illustration for tieflings in the PHB depicts a character whose tail looks to be thicker than her neck at the base and is at least as thick as her arm for most of that 4-5ft length. It is displaying an appreciable curvature, though, which suggests a decent degree of flexibility. The flavour given that a tiefling’s tail may lash about or coil around their legs also suggests to us that it has a reasonable range of motion. It would seem reasonable, based on the art and the description, to describe the tail as being about as a flexible as a snake with similar dimensions.
Control

The question of how much control the tiefling has over their tail is a bit trickier. The only example of tail behaviour we’re given is based on the tiefling’s emotional state; a tail that lashes or coils, sounding a lot like a cat’s does, without deliberate control. We can also extrapolate from what is not stated – the tiefling has no special racial trait which explicitly lets them make use of their tail for a functional purpose. That suggests that whatever control they do have over the appendage, it is not fine enough that they can interact with their environment using the tail anywhere near as adeptly as their other limbs.

Based on that, I’d judge that the best real-world animal to use as an example would actually be a cat. Cats’ tails are flexible and can lash and coil like the tiefling’s is described as doing – and a cat may deliberately flick their tail about sometimes, and tail behaviour is a helpful indicator as to a cat’s mood – but they aren’t capable of using their tail to pick things up, or manipulate their environment beyond hitting things (relatively gently).

A tiefling is more intelligent than your average cat, so you could imagine they could be a bit more creative in the use of their tail. They could probably use it to pick up reasonably sized objects that are both sturdy enough to withstand a bit of rough handling but not too heavy; potions and scrolls seem too small for the tail to be able to coil around enough to grasp, but I’d judge a spear/polearm or a bucket could be lifted (but not manipulated effectively) if the tiefling concentrates on what they’re doing.
Mechanical ruling

Ultimately I would probably rule that tiefling could deliberately flick/lash their tail about, or coil it around something reasonably sized and stationary, using the free object/environment interaction they get on their turn. That means they could do stuff like flick levers, behave inappropriately in bars, and knock your drink off the table with relative ease. I’d also suggest that a tiefling spending their action, and therefore concentrating their effort, on controlling their tail could use it to pick up reasonably sized objects, but could not manipulate them adroitly enough to do anything effective with them beyond carry them (no making attacks with a weapon held in the tail, etc.)