I would like to define monument as a mind-blowing man made structure which gives one a glimpse of a different era altogether during which it was built or was used. A monument or a historical remnants of an empire, rock cut caves, a majestic structure, have an archaeological treasure hidden in them. It is better to know few things before you pay a visit to any monument anywhere in the world.
Read a book written on that monument:- There are number of authors, architects, historians, geologists who have documented a scripted and printed versions of spectacular monuments u would like to visit, and also regarding their architectural heritage. A well written book on the history of the monument and that era would give u the same feeling as if you are present at that time if you sit nearby a wall of the sculpture and read that book. For example "The Monumental India Book" by Amit pasricha would be the good guide on the monuments of India with a great panoramic view of the captured monuments.
Check on blogs and videos:- Well, there are number of videos in you tube which would give u the visual idea well in advance before u go to the monument and make u familiar with that monument or a site. There are blogs written well with all the necessary details regarding the historical places, which gives the good tutor before visiting a place.
A Photography lesson:- One will sure feel to take a photo or make a video of the carvings, the wall paintings, the spectacular stone cuttings or the majestic structures they see. So, a better basic knowledge on using your DSLR would be handy to take pictures as you wish to. For example one should know the tricks of dim-light photography as it is not allowed to use flash in the caves of world famous Ajanta.
Check on Official website:- Now a days one can find a page or website on the monument with all the required details to be known like how to reach the place or if the entry tickets could be booked online. Also check if cameras are allowed to take photos and videos, and also check on the days the site would be open for a visit. For Indian monuments a website called "Archaeological Survey of India" would come to help.
Be the first to reach:- There are some places where you can't book online tickets in advance. So better be the first person to reach the place as you could avoid flocking tourists and could feel the essence of the place with a free mind.
Booking guides:- A visit to a 1000 or a 2000 years old structure would not be completed without a guiding person who knows and talks and explains every minute things about the place which you could still not find on any book or a blog page. So see that you also take a guide with you. Moreover in recent times one could take a self guided tours with an audio guide and accompanying map in a language of their choice.
Check on the additional places:- If there is a years old structure attracting people towards it, then that place would be definitely surrounded by a many more things which would witness and prove more about that place. So check with the locals and visit the other nearby places which gives much more evidence and knowledge on that monument, because it's better to gather all the information of a historical building.
Special occasions:- A historical monument or a site or a place would be linked with the local festivals or processions. So try to visit these monuments on the special occasions which in turn brings the old era back to the structure and will be much more exciting. For example if you really like to see the history lit with the luminous lights in the dark, then you should never miss the yearly celebrations at the monuments amidst hillocks like Hampi Utsav and Mysore Dasara.
P.S:- Please don't carve your own literature (your name or your loved ones name or the date you visited that place) and don't allow others also to write something on the centuries old structures as they have a lot of importance than what we think we know.