If you are venture backed just pay a PEO as someone else mentioned and be done, it is so much easier. These organizations are pretty expensive but they take care of it all and you just sign documents and approve transactions. Works even within the US for health insurance, workers comp etc, very simple for you and lets you focus on what is important and not admin tasks.

But to answer your question, at least partially and of course IANAL or accountant or tax expert. Second caveat of course, it will somewhat depend on your state, your company, the receiver & what Country they are in -- and your advisors knowledge/experience doing this.

Some basics:

Corporate Registration (as an employer not like a new corporation typically) in the Country and/or states you employ someone. Some Countries will require you to meet specific requirements, but most are pretty easy they just want to know the basics. In the Country (or US state) are likely additional filings you must do as well. For example in the US you will have to generally file (at least) quarterly reports with every state in which you employ someone, plus deal with workers comp, state taxes etc.

You may be required to meet government mandated pension requirements, paid time off, sick time, health insurance payments etc as well in the home Country if you are employing someone there. So it is always important to consider that as well.

You will file usually within those Countries and States every time you hire/fire or pay someone from their jurisdiction. This can be super simple monthly or quarterly reports much of the time, but there are specific instances where it is every payroll you must file. And taxes may or may not be due.

You need to track every dollar and where it came from and went to. This is so you can pass the foreign transfer audits should you ever be audited. This is usually pretty easy for corporations since you are tracking the money anyway. But in the past my accountant had us setup separate methods to track this all, both in the chart of accounts and then also in a physically separate account(s) where the money was put and transferred from. Using a separate account somewhat insulates you from the government seizing/freezing your primary operational bank account for "suspicious activity". At least if they seize/freeze that foreign transfer account temporarily it won't affect your operational account. There is entire strategies around this for corporations.

You will need to file a notice to the IRS on the person you are hiring and prove their Country of Residence and Nationality (usually using a passport). This is because even if a US Citizen lives abroad you must pay taxes for that person within the US during payroll. Also, there are other cases when someone may meet the criteria of having to pay US taxes. For example, if they travel to the US on any visa and do work within the US boarder you will owe US taxes on them.

You also will file notice of transfers with at least one other US agency (other than the IRS), IIRC homeland is who it is now, but you should check with an advisor on it specifically. Essentially what I remember having to setup here was we had to register with the agency, send them notice of any money being sent overseas when it exceeded a certain dollar threshold, and it was an odd amount, not something simple like $10k. And there are other rules on this part too that weren't that hard, but just again something else to manage and watch.

These are just some of the things, but I think it hits the biggest pain points. It isn't "hard" once you know what you have to do, it just adds time to what is usually an already overworked Founder. So it is best to hire it out where possible. Which is why I say don't do it if you are small or not backed, since the costs just add up. If you want to use someone overseas just put them on contract, and while you'll still have to file foreign transfer notices that is not nearly as much work as everything else, and in some cases your bank will file these on your behalf if you work with them. But someone I learned before, banks have their own notices they have to file on foreign transfers that are in addition to yours, so just confirm with them on it.

I have read and seen posts online from founders or people who say they don't do any of this and some saying none of it is required. I will just say I am not willing to risk large fines or worse over not reporting. Import/export businesses deal with this stuff all the time, it isn't new, but the rules do change fairly regularly so having good advisors is the best idea.

My objection isn't that the process is so hard or difficult, it is that it takes quite a bit of valuable time for an early startup to get things setup correctly. You have to guard your time very closely when you are starting, which is why I generally would not hire FTE's outside my home jurisdiction. Even when using contracts you still have some extra reporting requirements but they are a bit less time sucking.

edit: format