The best way to explore this city is by bicycle and by foot, no doubt! You can borrow a bike at the hostel and ask for directions but the Old Town (where we are right now) has so many small streets all around the temples.
However, Bangkok offers a wider mass transport system ranging from buses to river and canal boats, tuktuks, taxis and subway systems. Here are  just a couple of hints for those visiting for the first time in Bangkok.

Destinations:

Siam square (MBK, BACC, Jim Thompson, Central World, Platinum…)
Buses 15 and 47 from Ratchadamnoen rd (street with the big Democracy Monument round-about, 10min walk from the hostel)
Klong/canal boat from Pan Fah bridge near the Golden Mountain and stop at Jim Thompson’s museum Hua Chang pier or Central pier.
Lumphini Park and Sathorn (Patpong market, Cloud 47, Ghost Tower, Lebua Hotel…)
Bus 15 (see above) or Boat on the Chao Phraya river from pier 13 to pier 0. Catch a BTS Skytrain from Saphan Thaksin to Sala Daeng. (catch the boat at Phra Athit, the white fort with the park behind just 5min walk from the hostel)
Klong/canal boat from Pan Fah bridge near the Golden Mountain and stop at Central pier (last stop), then walk a bit or take the Skytrain.

Hua Lamphong central train station and China Town
Bus 49 and 53 from outside the hostel on the main street at Samsen or catch a boat (see above) and get off at pier 5.

Thonburi train station and Sirirat Hospital
Bus 516 and 79 both cross the river to Thonburi but you will have to get off at the first intersection then walk south towards the railroads. A better option is to take the river boat from pier 13 to pier 11 and walk passed the hospital to the station. Sirirat hospital also contains the Forensic Museum for those wanting to see some quirky things…

Taling Chang weekend floating market
Bus 79 from Ratchadamnoen street, opposite the nr.15/47 bus stations. The bus will cross the river to Pinklao. Alternatively you can hire a boat to bring you there but it will  cost considerably more.

Chatuchak or JJ weekend market
Bus 3 and 524 from outside our hostel on Samsen in the direction going away from Kao San rd. You can also take the bus 15 and 47 into Siam square and catch a BTS Skytrain to Mo Chit (last stop) or take the 53 to Hua Lamphong and take the MRT Subway into the market at Kamphaeng Phet. The market is open on Saturday and Sunday from 8ish to 19ish.

Southern Bus terminal (Sai Tai Mai)
Bus 516 just outside our hostel on Samsen on the main street in direction Kao San rd. A taxi will run at about 100THB (15km)

Eastern Bus terminal at Ekkamai
Bus 2 from the same stop as the 15/47 (see above)

Northern Bus terminal at Mo Chit
see the above description of the JJ market, it is the same direction!

BTS Nana station, Nana Plaza on Sukhumvite Soi 4 and Soi 11
Bus 2 (passes by Nana) or buses 15/47 to Siam square and then the BTS to Nana. The famous Nana Plaza on Soi 4 is just next to the BTS stop.
Klong/canal boat from Pan Fah bridge near the Golden Mountain and stop at Nana ( you will have to change to another boat at Central pier).

Khlong Toei market and Green Lung Botanical Garden
Bus to Hua Lamphong (see above) and then MRT Subway to Klong Toei. Please read up online when the market is actually open, it varies!
For the river crossing to the Green Lung you need to head over to Wat Khlong Toei Noi and cross the river in a nutshell :) On the other side you can rent cheap bicycles and head over to the Botanical Gardens

Saphan Phut / Memorial Bridge / Wat Arun
Boat from pier 13 to pier 4 (see above). Alternatively, use your legs and cycle or walk, it’s not far at all! Mondays it is no open however, just like many markets.

Train market / Talad Rot Fai
There are two, both are a little far away from this area. The closer one can be reached by MRT Metro. Get off at the Thailand Cultural Centre stop. The market is behind the Esplanade Mall and is open from Thursdays – Sundays from 17pm – 24pm. 

I am sure there are many more destinations not on this list, please ask day staff for more information. You can always hop on a taxi, motorbike taxi (fastest way in traffic) or a tuktuk for short distances. I know most want to experience the local way of traveling but believe it or not, Thais take taxis to (ask for a meter and make sure tuktuks don’t over charge you). To give you an idea, a Thai person would not spend more than a 100THB to China Town (3km) from Samsen Rd.

Rough estimates, sometimes it depends on how far you travel but you pay these on the transport:

River Boat  +/-20Baht
Canal Boat +/-7baht
Bus aircon +/-12baht
Bus regular +/- 7baht

BTS and MRT operate on coin machines and cashiers and it goes by distance. Get a day pass if you are doing many stops in one day!
You can check out www.transitbangkok.com. It has all the transportation methods of Bangkok documented.
 
Things to note and remember when you are visiting Thailand:


-Some temples require proper dress codes (long pants, long sleeves etc) so check first before you enter. 
-By the Buddhist Monk’s rules, a monk may not sit or come close to a woman. Some chairs in buses and trains are also reserved for monks. If you see one get in and you are in their  chair, be so kind and respect the rule. Also monks are not allowed to beg for money, sometimes some people think it is funny to dress up as one and fool tourists for donations.
-Touching people’s heads is rude unless it is for a blessing from a spiritual or older wiser person.
-Pointing at things with your feet is also considered rude and puts the other person in a lower position. A lot of people lay down on matts and have their feet up in the air. Normally having the feet above the head area is not very polite. Keep your feet lower and point at things with your hands!
-You end your sentences with a khrap (masculine) ka (feminine) and you are being very polite. Almost every sentence ends with those words if you listen carefully.
-Believe it or not, Bangkok has a law for littering and it can be up to 2,500THB for throwing something as little as a cigarette butt. Also many malls, walkways, skywalk etc are non smoking and they will fine you if they see you. The money will probably not end up in the government’s pockets but that’s  a different story…
-Walking on the street with a bottle of Alcohol is considered “low” and Thais will not carry their open bottles around. They sit down and chill and have a good time and that is considered ok. Also, taking your shirt off in public is considered rude. In touristy areas the Thais will not think much of it because they are used to it but it is still a rude thing to do.  As a matter of fact many go swimming with a T-Shirt and most men wear long pants even on hot days.
-Careful of lady boys. Some are notorious thieves and they punch like…well, men! You get your things stolen, stay calm, report stolen goods immediately, have the bank lock your cards and chill since there is nothing else you can really do…
-Careful with under aged girls, it is a serious offense and some girls claim they are older to then claim they are younger to get you in trouble…Prostitution is illegal in Thailand and can get you into deep shit!
-Most people do not consider most of these rules when they are drunk, hence they get into fights. Thais will not confront you one on one. Its all they can get against one and they bring things that hurt. Stay away from fights, drunk Thais do not think of consequences, neither do people from other cultures most often!
-Don’t argue about 20THB in a taxi or tuktuk ride, some taxi drivers go nuts for a little bit of money. It is not worth the 2cents to get your arm chopped off. If you are suspicious of higher fares than regular, weird behavior etc, just take a picture of their number plate and taxi license in the front of the co-pilot seat and have it reported to a Tourist Police station or call 1184!
-Watch out on overnight bus rides, there are a thousand of stories online of people having their stuff stolen. Trains are generally safer, they carry police as well. TukTuk drivers or people talking to you on the street presenting themselves as teachers or being overly helpful when not asked, saying this colour of the flag and that number plate or that temple is closed come see a better one which is free…these are all people trying to lure you into doing  something you did not want to do. I guarantee it!

Regardless of those points, Thais are otherwise super friendly people and it may seem weird some would consider scamming, fighting or stealing  from you but like in every country, there are some assholes.
Stay focused, respect everyone around you, be friendly and polite in all ways possible, learn some Thai words and you will have the best times ever in Thailand because they are very generous human beings, always trying to help and make sure you feel at home. Which you will…