The Triveni Sangam is the junction point of three rivers - Ganga, Yamuna, and Saraswati (which is a mythical river, supposed to have dried up milleniums ago) Both Ganga and Yamuna are extremely revered rivers in Indian mythology, and hence the confluence point of these rivers has attained extremely high religious importance.
According to Hindu mythology, taking a bath in the holy Sangam is supposed to flush away all of your sins and free you from the cycle of rebirth. While we can't say much about that, the Sangam itself is a really pretty and peaceful place to visit. If you take a boat ride to the gently flowing waters of Ganga and Yamuna, you'll be able to clearly make out the difference in colours of water from the two rivers. There are also makeshift wooden banks made at the Sangam, so if you want you can go take a bath right at the confluence point. The water is generally clean enough at the Sangam for a bath, specially during the winters, and not very deep, so it's fun to take a dip in water here.
The Triveni Sangam is an extremely holy site, and there are a number of myths associated with it. For eg, it is believed to be the place where drops of nectar fell on earth during the battle between the Gods and the demons - this is the story of origin of the Kumbh Mela which is held here every 12 years.
You would find a lot of pandits sitting by the side of river doing different kinds of pooja for people - for the well-being of their families, for prosperity, etc. A lot of people visit the Sangam for immersing the mortal remains of their loved ones, and you could see them performing poojas by the side of Ganges.
Like most religious sites in India, you need to be extremely careful while talking to the pandits here. If you are here for any religious poojas to be performed, be sure to talk to the pandits about how much they will charge you before actually asking them to do anything for you - otherwise they will almost certainly quote an absurdly high amount after the pooja. Do remember that the bargaining is extremely heavy - if they quote 1,000 for something you might be eventually be able to get it done for 100.
If you are not here for any religious purpose, and just want to visit the confluence point for pleasure, be very clear with the pandits and stay totally clear of them - while being as respectful as possible. The pandits here are highly revered, and they frequently team up with the boatmen, so if you are rude to them you might end up having to fight with everyone around you. For the same reason, a lot of boatmen who ferry you to the Sangam might try to force you to get some pooja or the other done - unless you really want to do that, be very clear that you don't want any religious services at all.
For boating, the bargaining will start with an absurd amount - say 2,000 for a 1-hour boat ride - but if you bargain heavily you should be able to hire a full boat for a round-trip ride to Sangam for no more than 500.
Well connected through main city via all means of transport. The most comfortable way is to book an Ola cab which will drop you to the banks of Sangam, from where you can take a boat/ferry. Otherwise, you can take a tempo/auto-rickshaw to reach there as well.
From the banks, you can hire a full boat for a return trip to the Sangam area (keep in mind you'll have to bargain heavily - during off-peak season, a full boat ride shouldn't cost more than Rs 400 for the return trip)
Carry camera, torch light and fully covered clothes, proper footwears, munchies, beverages and water along.