Good Day to you!
I’’m certainly no tax expert, but because a lot of people hear me asking questions, they naively imagine I know the answers, so I’ve had to do some research -no guarantees I'm 100% accurate!
The forms for applying for NPWP are allegedly available on the web, so use the search engine, or get your employers to get you one. A lot of employers seem to have a tradition of doing their utmost of avoiding tax payments, so you may need to push them. The deadline for applying has been extended from New Year to the end of February.
My colleagues and I were asked to provide documentation e.g. passport ID pages, Kittas, and a form to be signed by the local RT, though since we didn’t understand the latter requirement, we failed to provide it nd the NPWP cards were issued anyway.
Our cards are yellow, but a university expat friend and his colleagues got grey cards, being advised that was the correct colour for expats, whereas we got bright yellow ones.

There is argument about what income constitutes tax. Salaries, obviously, and interest on savings. Not sure if banks deduct that or whether we have to go back over our bank deposit books and calculate it. Those charming gals at BCA customer  service desks in their big hq office on Sudirman may be worth a visit.
But there are grey areas.  , esp on housing allowance,which one employer has assured workers is not taxable. Others assert it is.
I append a part of internet info which may explain.

"Any salary paid to you for your current position, whether it be onshore or offshore
Dividend and interest income, both onshore and offshore
Rental income both onshore and offshore
Capital Gains from Sale of Property, both offshore and onshore
Benefits in Kind are generally excluded: Housing, Cars, School fees, as well as income from inheritance.

However, if your company pays you for housing in one lump sum, and then you make the payments … the tax office may construe that lump sum as income. In this case, it may be better for your employer to pay the housing costs direct to the landlord. You take the money as an advance, not as housing allowance. The company then expenses one month at a time as housing, which is then treated as a fringe benefit.

Credit is given for income tax paid overseas, subjected to limits and perhaps dependent on double taxation treaties between Indonesia and your country. You may also receive credit for tax taken on interest income for local bank accounts and time deposits and other interest earning methods that are taxed.

Since income from Overseas Investment can be taxed, it is best to consult your accountant ………"

So seems you need to check that any income you obtain back home is taxed and have that info ready, though I’ve heard that they may tax you again here anyway, esp if tax rates vary from land to land.
All major Western countries have ‘double taxation’ agreements with Indonesia (Britain, America, NZ, Aussie and Canada) but from what I’ve heard, although our various embassies claim to represent our governments, they are loathe to offer any help to citizens (on tax matters – if you get jailed, they’ll come and visit you!). I suspect it depends on the individual. Consuls and other staff change and I know of one case where the change has resulted in a much more approachable attitude.
There is a wealth of knowledge among people on IM, so I  hope others will come forward to augment and if necessary correct the above. Good Luck!
PS I’ve heard it said that there are so many new NPWPs that the bureaucrats will take months to get around to us wee fellas, but since we are the most vulnerable, that may not be so!