Usually legislative bodies will have some sort of orientation handbook or process for newly elected members. In your example of New Hampshire this is actually written into legislation - Title 1 Chapter 17C of the New Hampshire Revised Statutes establishes a committee on legislator orientation with a responsibility:
- To prepare, print and distribute a legislator's manual before the
legislator's orientation program scheduled pursuant to paragraph II in
the even numbered years which may consider the following: The house
rules, the joint house and senate rules, suggested rules for procedure
of legislative committees, a map of Concord, floor plans of state
house, a department directory, parking, the procedure for filing a
bill, the location of committee rooms, an explanation of the telephone
system, a roster of members, food and lodging locations, rules on
mileage, tax status of mileage, caucuses, election of certain
officers, election of attaches, operation of the organizational
session, events on the first day of the regular session, salary
payments, state library facilities, legislative services, and a brief
sketch of parliamentary procedures.
- To prepare and run a
legislator's orientation program primarily for new legislators which
shall be held in Concord between the date of election and the date of
the organizational session.
This information is usually public - in New Hampshire's case the orientation manual itself can be found here, with further orientation information available here, including schedules for both houses of the legislature, a list of legislature rules, various ethics policies, as well as more mundane information such as parking locations.
Most state legislatures implement something similar; the National Conference of State Legislatures has conducted a survey on this topic, finding that "nearly every
legislative body gives this task pre-session priority and conducts an orientation conference of some dimension".
Outside of the US, to give one example, the UK House of Commons produces a fairly comprehensive Members' Handbook which covers everything from instructions on how to table questions, to the rules around speaking in debates, to the location of smoking areas. This is supplemented by the New Members' Guidebook which provides more concise information for the newly elected Member of Parliament.