The procedure of amendment makes the Constitution of India neither totally rigid nor totally flexible, rather a curious mixture of both. Some provisions can be easily changed and for some others, special procedures are to be followed. Despite the fact that India is a federal state, the proposal for amending the constitution can be initiated only in the House of the Union Legislature and the State Legislatures have no such power.
In case of ordinary legislation, if both houses of the Parliament disagree, a joint session is convened. But in case of amendment of bills, unless both the houses agree, it cannot materialize, as in such cases there is no provision for convening the joint session of both the Houses of the Parliament.
In fact, there are three methods of amending the Constitution. But Article 368 of the constitution which lays down the procedure for amendment mentions two methods.
1) An amendment of the constitution may be initiated only by the introduction of a Bill for the purpose in either house of Parliament and when a bill is passed in each house.
i) by a majority of total membership of that house.
ii) by a majority of not less than two-thirds of the members of that house present and voting, it shall be presented to the President who shall give his assent to the Bill and there upon the Constitution shall stand amended in accordance with the term of the Bill.
Most of the provisions of the constitution can be amended by this procedure.
2) For amending certain provisions a special procedure to be followed,
(i) a Bill for the purpose must be passed in each house of Parliament by a majority of total membership of the house,
(ii) by a majority of not less than two-thirds of the members of that house present and voting and
(iii) it should be notified by the legislatures of not less than one-half of the states before the Bill is presented to the President for assent.
The provisions requiring this special procedure to be followed include- (a) manner of the election of the President, (b) matters relating to the executive power of the union and of the state, (c) representation of the states in Parliament (d) matters relating to the Union Judiciary and High Courts in the states (e) distribution of legislative powers between the union and the states (f) any of the list in the seventh schedule (g) provisions of Article 368 relating to the procedure for amendment of the constitution etc.
3) There are certain provisions which require simple majority for amendments. They can be amended by the ordinary law making process. They include (a) formation of new states and alteration of areas, boundaries or names of existing ones (b) creation or abolition of Legislative Councils in the states (c) administration and control of scheduled areas and scheduled Tribes (d) the salaries and allowances of the Supreme Court and High Court Judges (e) laws regarding citizenship etc. It is significant that the laws passed by Parliament to change the above provisions would not be deemed to be amendments of the Constitution for the purpose of Article 368.
(If still there is a problem in understanding, questions can be asked in comments)