The only public transport to and from the airport is the train. There is no buses at all. So a train or a taxi is your only method. I found the train method works fine but it of course depends on the times of your flights. There are around ten trains a day in each direction so it works out as roughly one train every one to two hours. I have attached a PDF train timetable but it sounds like you have already looked so maybe a taxi works better for your times.
There are always taxis waiting in the taxi ranks at the airport. So you can just use one of them. I do not think there is any need to pre book. The taxi drivers usually take cash only so make sure to have some cash.
The price is generally between EUR15.00 to EUR20.00 for the taxi journey from the Airport to Podgorica where as the train is EUR1.20 for this journey. So if you want to save a lot of money and pay just EUR1.20 then it might be worth waiting around at the airport for your train. I personally would as you save so much money. There is a cafe and a shop and some seating in the airport that you can use if you have a while for your train.
Podgorica has local city buses but they do not serve the Airport unfortunately but the website is here:
Glavni Grad Podgorica
podgorica.me
Most younger people speak English so if you need to talk to someone look for someone younger. Most older people do not speak English at all. Generally the younger the person the more likely they are to speak English and the older the person the less likely they are to speak English is what i have found. German is spoken among many older people as it was taught in schools. Russian is also spoken among many older people as it was also taught in schools and also among some younger people too as there are quite a few Russians living there. It has always been a popular tourist destination for Russians to visit. But as for English enough people speak decent English for you to easily manage. It is not that difficult to get by with English in the country.
The main language spoken is Montenegrin (in fact Bosnian and Croatian and Montenegrin and Serbian are all the same identical exact language but for political reasons they are considered four separate languages) and is mainly written in the Latin script these days but the Cyrillic script is still used in some places and among older people.
The international trains to and from Serbia (which also pass through Bosnia & Herzegovina too) are locomotive hauled and these can be used for domestic journeys as well. The local domestic services are a mixture of the modern CAF Civity units and very old RVR ER31 type Soviet built Elektrichka units.
The railways consist of the mainline from Podgorica to Bijelo Polje at the Serbian border and the mainline from Podgorica to Bar and the branch line from Podgorica to Niksic too. There is also a fourth line from Podgorica to Tuzi at the Albanian border but this one does not have any passenger trains running on it.
You can purchase ticket offices at the railway stations or onboard the trains. Most smaller stations (including the airport station) are unstaffed and there are no TVMs anywhere so from most stations you have to purchase onboard. First Class tickets are available but not really necessary. Tickets prices are extremely cheap by British standards.
Some examples of the train fares:
Airport to Podgorica: EUR1.20 (STD) / EUR2.00 (1ST)
Airport to Bar: EUR2.00 (STD) / EUR2.80 (1ST)
Bar to Airport: EUR2.00 (STD) / EUR2.80 (1ST)
Bar to Podgorica: EUR2.40 (STD) / EUR3.60 (1ST)
Podgorica to Airport: EUR1.20 (STD) / EUR2.00 (1ST)
Podgorica to Bar: EUR2.40 (STD) / EUR3.60 (1ST)
Purchasing tickets is cash only. It is a very much cash based country still. So it is a good idea to have cash with you. They use the Euro there.
If you board at any of the five stations that have ticket offices - Bar / Bijelo Polje / Niksic / Podgorica / Sutomore - and the ticket office is open then there is a small EUR1.00 surcharge to purchase a ticket onboard the train. But when boarding at any other station (such as the Airport or the hundreds of other stations in the country) there is no surcharge at all to buy onboard.
There are no online tickets or e tickets or m tickets. You just simply purchase at the station before your train or onboard the train.
This is the railway company website:
Željeznički prevoz Crne Gore. Informacije o redu vožnje, lokalnom saobraćaju, međunarodnom saobraćaju, javnim nabavkama, kretanju vozova i novostima.
www.zcg-prevoz.me
They have a basic app here as well:
The website also has a list of departures and a basic journey planner.
I have attached the current up to date timetable and fares PDF document for the railways. This has all the timetables and fares. You might want to download and print a copy. This will enable you to see the timetables when you have no internet access.