There are 3 steps that interact together and lead to memorizing those verbs and to eventually being able to use them naturally and fluently in speech and written text.
1- Understanding the usage of the verbs ,when and how to use form the combination of 2 verbs . What are the auxiliary verbs ? What is the infinitive ? the gerund? etc..
2- Practice using them through grammar exercises, speaking , listening ,reading and every possible method .
3- This will lead on the long run to memorize them. Memorizing is the natural result of initially understanding the concept than practicing it intensively enough.
@ Richard, it is not memorizing Xusha's information directly ,rather understanding the way sentences are formed, applying those verbs and exercising their usage continuously, that will lead eventually to memorizing them. As a native English speaker you learn at a very early age initiative recognition of the words and form usages before even having developed cognitive skills. So the application of those verbs in their different forms seem "natural" and don't apply much analyzing to their structures.
However for an English language learner they will depend more on their cognitive skills which requires analyzing and linking information to understand the concept, then through constant repetition manage to memorize its usage.
This applies for an academic learner pursuing an English language course , however it is important to mention that others could through merely learning words from mouth , mingling a lot with natives , listening a lot to English through watching movies ,hearing songs etc,manage to memorize those structures much like the way a native speaker does at an early age.
This will not be however sufficient for everyone to achieve an adequate level of applying the structure. In general a mixture of both ( theoretical and practical usage) could lead to the best results.