They are very similar but amend is used when we change something in a formal document. For example: "he amended his statement to the police after he viewed the scene of the accident". Parliament "amended the law" - note this is a neutral factual statement - it does not mean "improve" the law. We can also change, modify and alter documents. We can alter clothes to make them fit better but if we change clothes we are simply removing one set of clothes and putting on a new set of clothes. We can modify, change, alter and amend plans. We can change our mind but if we alter our mind we are probably on drugs!
I suggest you find examples of the use of each of these and see the contexts in which they can be used.