Do your homework. Try to learn something about that era before starting a novel, drama or poetry book. Use the internet to read articles about the author of that classic, characters and events. For example if you have selected “A tale of two cities” by Charles Dickens then you should know something about the French revolution.
Start with those books that are not lengthy and wordy rather stick to the short one. You better start with short stories or poems as their format will be easy to understand and you will not have to spend too much time to finish one item.
Similarly if you are reading a lengthy book then be patient and consistent. Most of the beginners get frustrated and leave reading classic literature.
Do not read a classic just because it has been declared one. If you have decided to start reading a drama or novel then your approach should be to read it for enjoyment and education. You may watch movies based on novels and dramas as you will feel more connected to these classics.
Do not try to finish a book in just one sitting rather make it a habit to read a couple of pages before you sleep every night. This will help you to understand the story structure and ultimately you will enjoy this experience.
You should read only one book at a time and avoid reading modern prose if you have a piece of classic literature on your study table. Try to enjoy the language if you are not familiar with old terminology. Take it as a learning process and you will start enjoying afterwards.
Most of the people make a common mistake that they start evaluating classics with a modern attitude and approach. You should keep that era in mind as it will be really helpful to understand the story, characters and incidents.