Bangkok has a modern train system, but some lines operated independently.
The SkyTrain Green lines require a single trip ticket or an Orange (Rabbit) card which can be refilled.
The MRT Blue (underground) line requires purchasing a single trip token, or a Blue "visa" card which can be refilled; the Blue line will also accept some "wave" cards.
Both cards require a process involving presenting your ID to obtain them; you may only want to do this if you will make a number of train trips.
BEWARE: queues can be long at peak times to buy a single trip ticket, or to top up your card.
Asoke intersection (one stop North from QSNCC) can be especially busy at peak times.
Airport Rail Link goes from "Suvarnabhumi Airport" into the city; change at Makkasan for the MRT Blue line or at Phayathai (end of line) for the SkyTrain green lines.
It is easiest to buy a token separately for each trip
Grab is the default "Uber" styple app to use here in Bangkok, and generally works well.
LINE MAN is used by many locals, and is generally considered safe and reliable. Please note: LINE app must be installed to use it; also, LINE MAN may not be available in your app store.
Street taxis are plentiful and cheap, but the condition of individual vehicles can vary quite a bit
A small red or green sign in the front curbside part of the windscreen indicates they may be available
Taxi drivers may refuse trips, especially at certain times of day
Sometimes they may ask for a set fare (more often happens for non-Thais)
Taxi drivers often have little change, and often can't break a large bank-note; it's always easier if you have smaller notes available when paying
Google Maps also works here and can give you a good estimate of how long a trip may take
BEWARE: Traffic can be very slow at certain times of day, particularly during peak times.
Some routes are typically worse than others at peak times eg. travelling North from QSNCC to Asoke will be slower than if you travel from Asoke to QSNCC
In practise, tuk-tuks are used much more by tourists than local people
Fares are often more expensive than taxis and need to be "negotiated"; they are typically around 80-150 Baht
Very convenient and can be much quicker to get around
Fares are negotiable ~50-120+ Baht
BEWARE:
You have come to Thailand, NOT to an alternate universe where the normal rules of physics and common sense have been suspended
There is a very high road accident rate in Thailand, especially for those travelling on motorcycles
You are legally obliged to wear a helmet, and it is obviously more safe to wear one
Check that your travel medial insurance covers you for travelling in this manner; many have found out the expensive way that it does not
Overall Bangkok is generally safe to walk around
Ensure you stay well hydrated; bottled water is cheap and easy to buy at convenience stores eg. 7-Eleven
BEWARE:
Some roads don't have foot paths, and some back streets require care when walking, especially at night when you may not be clearly visible to a vehicle
Motor cycles often use foot paths - watch out for them
Motor cycles often travel the wrong way (illegally) on a street; look both ways before crossing a street and constantly be aware that a vehicle or bike may appear unexpectedly