I have some understanding on g-force. But never come across how much g-force acts on a passenger who is traveling in a plane, especially when taking off.
There are two basic classes of G-load; static and dynamic. The difference is time; static loads are those placed on the airframe and its contents during relatively sustained maneuvers like climbing, banked turns, etc. Dynamic loads are transient; turbulence and touchdown are the two big ones. Which one we're talking about is very germane to the question; most maneuvers deal primarily with a static load caused by the change in direction of travel over a sustained turn or pitch-up, however dynamic loads from turbulence while maneuvering must also be accounted for.
Also very relevant is the weight of the aircraft at the time of a g-loading event; g-forces are always a multiple of this mass relative to the force of gravity on that mass. The weight used for rating purposes is usually the aircraft's max take-off weight, because this is the heaviest that a plane is expected to be while flying (and thus subject to maneuvering loads), and so the most pessimistic.
For static G-forces, the 737 class operating G-range is between +2.5g to -1.0g at MTOW in "clean" configuration (reduced to between 2.0-0.0g under full flap). Multiplied by the 737-800's MTOW of 79,000 kg (174,165 lbs), we get a critical number when talking about such things, which is known as the "design load limit", which for the 738 is 197,500 kg (435,412 lbs). The aircraft's combination of mass and G-loading should not exceed this number.
This means the aircraft can, theoretically, withstand much higher g-forces on a ferry flight when there are no passengers or cargo; at the 738's operating empty weight of 41,145 kg (90,710 lbs), the DLL represents a maneuvering of 4.8g.
You are unlikely ever to get anywhere close on the average passenger flight in a sustained maneuver; such a banked turn would be hard even for the pilots to sustain. A "steep turn", using wing bank in the 20-40* range, is about the steepest maneuver you're likely to experience on a commercial airliner, when ATC asks for a "nonstandard turn" during approach or departure to fit the plane through a gap in traffic. Even in this maneuver, you're unlikely to feel more than about 1.25g of force pushing you more firmly in your seat.
The aircraft, however, can take even more. The DLL is the "safe working load limit" of the aircraft under normal conditions, which pilots and airlines shouldn't exceed. To prove the airframe can handle that load, every flying airframe is "proofed" to 1.125x the DLL (representing a 2.8g load at MTOW) which it must survive without structural compromise ("bending"). A sacrificial example of the airframe is also failure-tested to the "Design Ultimate Load", a static load of 1.5 times the DLL (representing a 3.75g load at MTOW); it must withstand at least this load for 3 seconds without structural failure ("breaking").
FAA regs (Title 14 Part 25) state that any "Transport"-category aircraft (encompassing virtually all commercial airliners) must be demonstrated to withstand a loading of at least 2.5g at MTOW, but do not have to be able to withstand more than 3.8g at MTOW. In addition, there is a general requirement that the aircraft must be able to withstand any vibration, buffeting or turbulent forces that could occur at any speed up to the "design diving speed" VD, and must withstand any additional forces that could be imparted to the aircraft by a failure or malfunction of any part of the flight control system at speeds up to the airframe's "design cruising speed", VC. So, all airliners from the little Bombardier narrow-bodies up to the A380 have to be able to at least match the 737 in their g-loading capabilities.
I can't find solid references, hopefully someone will come along who can.
A 30 degree bank, the most you will normally experience, exerts a force of 1.15g, or 0.15 greater than normal acceleration you feel when motionless. The autopilot is generally designed to begin descents and climbs with no more than 0.25g and are generally calibrated to manoeuvre in 0.25g increments. A solid rotate or a firm landing might generate a bit more.
It's reasonable to work on a range of around 0.75 to 1.25gs. Anything more than that would be uncomfortable for many people. You should only experience g outside that sort of range in heavy or severe turbulence.