Deep breath...

The registration document?  (They usually state 'fuel type' somewhere).
The model designation?  (If it has a 'D' somewhere, it'll be diesel).
The dashboard/cluster. Diesels usually have a 'curly glowing wire' warning light in the cluster that illuminates when you first turn the ignition on.  These are for the Glow plugs fitted to diesels.  (Though some very recent diesels don't have them & they don't stay on for long once the engine is warm).
The rev counter.  They usually max out at around a 5k red line if diesel.
The fuel gauge.  Usually says 'Diesel' if diesel.
The fuel filler.  Often has a sticker saying 'Diesel' or something with a 'RON' or unleaded.  The latter two are petrol.
Looking in the engine bay is often little help, unless you're really into cars...  Petrol cars don't have ignition leads any more & the engine is often covered by plastic trim panels.  The fuel injection systems (assuming you can see any of it!) are difficult to tell apart, though diesel injectors are bigger than petrol ones. 
If you can find the spark plugs or a coilpack, it's petrol.
Start it.  Diesels are a bit more 'clattery', though so are worn petrol engines....
Smell.  Diesels smell of diesel.  Petrol smells of... (wait for it..!) Petrol!  Open the filler flap & savour those aromas!   (I did say Deep breath...!).
Take it to a garage/shop.  Ask: "Is this car petrol or Diesel?" 
If all else fails, (& I really do notrecommend this!):

The final option is to fill it with fuel. 

Petrol in a diesel & it'll eventually stop, (assuming you could start it!), probably with damage to the fuel system if you're unlucky.   If you're very unlucky & insist on driving it any distance, you can grenade the engine.

Diesel in a petrol car?  Clouds of smoke.  Lots of pinking/pinging (=pre-ignition).

Both these options will require that you drain off the fuel system & replace filters.  Possibly much more work will be needed if you put petrol in a diesel.‎
‎https://www.quora.com/How-can-you-tell-if-a-car-has-a-diesel-or-a-petrol-engine
‎

Incase

When I thought I have seen it all from autosbay, then comes this thread
Very soon I will see "how to know if your car is Honda or Toyota"

@ colossus2 no information is too small or too big, just that little tip might be helpful to millions of people

AutosBay:
@ colossus2 no information is too small or too big, just that little tip might be helpful to millions of people

You know say I sabi whine you

If it is hybrid nko?

Abi all out electric?

or one simple way open d fuel tank and smell it .lol

daamazing:
or one simple way open d fuel tank and smell it
.lol

Guy u dey vex oooo. I no wan laff belle dey fain me U no wan hear all those long procedures.. LOL

onward4life:


Guy u dey vex oooo. I no wan laff belle dey fain me U no wan hear all those long procedures.. LOL

lol

colossus2:
When I thought I have seen it all from autosbay, then comes this thread
Very soon I will see "how to know if your car is Honda or Toyota"

Next, how to know if your vehicle is an Okada or a car

@ mastro I concur

Some car manufacturers also have some writings usually at the back of the car to indicate the car has diesel engine. Here are some of them.
Ford- TDCi
Hyundai/ Kia - CRDi
Fiat, Alfa Romeo, Lancia - JTD
BMW - 320d, 528d,730d
VW/Audi - TDI
Toyota - D.4D
Mercedes-Benz - CDI, BlueTEC
Nissan - XD, TD
Land Rover - Td6/TDV6
Honda - i-DTEC

phibetakappa very informative

@Autosbay..... Your posts are always educative, thanks!!