Hey.

In 2019 the BHU LLB was conducted on May 14, 2019. Hence you can expect the exam to be conducted on the month of May. And the application process to begin in the month of February- April. The tentative or final schedule for 2020 is not out yet. The test centres were in 45 cities for the offline mode and in online mode in 115 cities. 

For preparation You can use an all inclusive guide like Universal's guide to LLB and CLAT which includes basics and practice questions for all these topics which can also be used for other similar entrances. You can also use Arihant's guide to BHU LLb. Other than that you can refer to previous year question papers for each entrance for a better guidance. For current affairs and verbal section the Hindu is considered as the best newspaper. You can use Word power made easy- Norman lewis for vocabulary. You can use R.S aggarwal'a books for Logical Reasoning or quantitative section in case you need a separate book other than universal's guide. You won't require a separate book for reasoning as the level isn't that high. Univeral/arihant woukd be fine.  Make sure you practice a lot using previous years question papers for a better rank.

Best of luck!