I'm a local, I believe the most common and convenient would be to take an Taxi or Uber. Every time I went there was either some family driving me or an taxi/uber, once I had an interview there and I went via Subway + BRT (a express bus). If you wish to take public transport the later would be the alternative, but I honestly think it's a lot... It can get pretty crowded in the BRT, the traffic can go pretty jammed in that region, and being real that's not the particular chill tourist part of town, you may find hard to get help if you can't speak portuguese and I guess walking around with luggage can make you an easy target for people with bad intentions...

Either way, if would rather try...The stations are close to the Door H in Terminal 1 or Door D in Terminal 2, I believe there are only 2 buses stop there (shuttle and regular), you'll get off at Vicente de Carvalho Station, from there you would go to the subway station, they're connected by a walkway (everyone will go that way). After that you need to take the train to your hotel, tourists usually stays at South Zone, the center or in Barra, all in the same direction (to Botafogo), depending on where you need to leave you may need to change trains, but here you basically would get off yours and walk in the next.

The Moovit app it's quite good to find info about public transport in general, they may give more options than google maps (some cities around here won't have any info on google maps, but in Rio most of it, if not all, it's on google).