So the party has just recently said screw it to going into the caves to find a long lost artifact they were hired to find and decided to spend money on ordering a recreation from a Smith. They then decided to make back the money by writing and performing a play 

I'm at a bit of a loss on how to run this section and keep it interesting and fun for the players. My plan is to make it skill check based for just about anything they do, note down their success and failures and use that to determine the outcome, in this case how much money they make back. 

Example.

The bard ateempts to act out a fight with someone. They roll a performance check and pass. Note down one pass and let the action continue. 

Does this sound like it might work. Has anybody had any sort of experience with this. Suggestions welcome.

You might want to look at the skill challenge article posted recently, it seems to suit your need https://www.dndbeyond.com/posts/285-traveling-with-style-skill-challenges

Interesting read. Definitely going to have to digest that info for later

If the artifact is long lost how are they expecting somebody to recreate it? Do they have the detailed diagrams and notes, because a simply picture would not be sufficient. I mean if the artifact could just be recreated, why would the person hiring them actually hire them if they could just spend the money for a recreation? I think that should be addressed and have one of them do an Int check with a low DC to realise the futility of this endeavour.

As for earning coin for things like performing on stages, this probably seems like something you can explain quickly through downtime and there's info the PHB and XGtE for info on using skills in downtime for making money.

If the performance checks start to go badly, you should have a heckler in the audience

The artifact has been lost but not the details on it. The PC were smart enough to do some research before leaving to find it. And they hired the best Smith to make a replica. Rhetoric ly decided to do this after they got scared and ran away from the caves ( the quest giver found the location). 

While I could explain them performing and the outcome It seem really boring to do so. Its something fun they can get some laughs out of.

Quote from TexasDevin >>

If the performance checks start to go badly, you should have a heckler in the audience

 That's a given

Taking a step back from the mechanics of this, I wouldn't let the PCs get away with what they've done. Let them think they've pulled the wool over the eyes of the quest-giver, but sooner or later they're going to have to act like adventurers. Perhaps somebody else will find the artifact and both shame the PCs and do something terrible with the original.

Aside from that, it isn't easy to fake an artifact. Unless you have arcanist's magic aura, a simple detect magic spell will prove they've forged the artifact. Even if they can disguise the aura, sooner or later the employer should be able to work out that the object isn't doing what it's supposed to do.

Quote from Heartofjuyomk2 >>

Taking a step back from the mechanics of this, I wouldn't let the PCs get away with what they've done. Let them think they've pulled the wool over the eyes of the quest-giver, but sooner or later they're going to have to act like adventurers. Perhaps somebody else will find the artifact and both shame the PCs and do something terrible with the original.

Aside from that, it isn't easy to fake an artifact. Unless you have arcanist's magic aura, a simple detect magic spell will prove they've forged the artifact. Even if they can disguise the aura, sooner or later the employer should be able to work out that the object isn't doing what it's supposed to do.

I get the impression, since this can apparently be replicated by an ordinary smith, this artifact in question is not a magic item, just a relic. I think they're using artifact in the original definition of the word not as a D&D term.

I second the recommendation of making the production a skill challenge, perhaps modified a bit - I love skill challenges ever since they were introduced in 4E and use them pretty regularly.

You could expand the scope of the skill challenge to include the preparations leading up to the night of the performance; for example, maybe a player rolls an History check to find an especially popular tale to base the play upon, and another player rolls a tools proficiency check with their Alchemy set to create some really cool stage effects. Definitely let the players take the reins! I'm tickled pink by their lateral thinking with this mission, and I'd want to encourage/reward it with the opportunity for more creativity on their part. (Though I also agree with Heartofjuyomk2 that their creativity should come back to bite them in the ass later. That's part of the fun.)

Sorry yes I'm using the term artifact interchangeable with relic. That's how I described it in my notes.

And yes they won't get away with this as flawlessly as they think. They went to one of the most renowned Smith's, so his makers mark will be somewhere on the peice. That's going to come and bite them later on somehow.

Quote from Nat_30 >>

I second the recommendation of making the production a skill challenge, perhaps modified a bit - I love skill challenges ever since they were introduced in 4E and use them pretty regularly.

You could expand the scope of the skill challenge to include the preparations leading up to the night of the performance; for example, maybe a player rolls an History check to find an especially popular tale to base the play upon, and another player rolls a tools proficiency check with their Alchemy set to create some really cool stage effects. Definitely let the players take the reins! I'm tickled pink by their lateral thinking with this mission, and I'd want to encourage/reward it with the opportunity for more creativity on their part. (Though I also agree with Heartofjuyomk2 that their creativity should come back to bite them in the ass later. That's part of the fun.)

 I like the idea to include set up in the skill check, gives the other players that aren't really taking to much part in the performance something to contribute.

And yes I do need to reward the creativity this missiin. I want to try rewarding them in game and out of game. But they did make one mistake when they hired a world renown Smith to create the replica. The makers mark will eventually be found and then they are going g to get what's coming to them

Firstly, thank you for allowing your players to derail a quest! (Even if you have a 'come back to bite you' surprise later down the line).

As an idea, could they perform a famous play that already exists in the world? Could they be hired as actors for a local playhouse, and play relevant parts? You could give them a script to learn, with simple responses to prompts, and roll skill checks accordingly.

If the players forget a line, they could roll a relevant roll to see if their character remembered some or all of it.

Could be a fun way to get everyone involved, with a bit more structure to the proceedings, if everyone had a part to learn. If they perform incredibly, they could be become famous, earn the praise of the locals and return on future nights for future plays, with bigger audiences!

Quote from Chequers >>

Firstly, thank you for allowing your players to derail a quest! (Even if you have a 'come back to bite you' surprise later down the line).

As an idea, could they perform a famous play that already exists in the world? Could they be hired as actors for a local playhouse, and play relevant parts? You could give them a script to learn, with simple responses to prompts, and roll skill checks accordingly.

If the players forget a line, they could roll a relevant roll to see if their character remembered some or all of it.

Could be a fun way to get everyone involved, with a bit more structure to the proceedings, if everyone had a part to learn. If they perform incredibly, they could be become famous, earn the praise of the locals and return on future nights for future plays, with bigger audiences!

 Are they actually playing if they don't derail you stories.

I understand what your saying about structure and getting people involved. It also gives me a bit more control over a situation. 

Also on the flip side of being famous they might perform so badly that they are never cast in respectable roles again. That would be devestating for the bard, she has spent ages trying to build her fame