Sounds like you need some pointers for the accidental DBA: https://www.sqlskills.com/help/accidental-dba/
There is also a book from Jonathan Kehayias: https://www.red-gate.com/library/troubleshooting-sql-server-a-guide-for-accidental-dbas
I'd suggest starting with Brad's Sure DBA Checklist. It's a good starting point for understanding all that you have to do. After that, monitoring is a huge topic. There is a lot involved. Personally, I'd suggest getting a third party tool because you'll be much better off taking someone else's work and applying it. But, if you have to do it yourself, start small and grow slowly. You can impact performance by monitoring, so you want to be very cautious.
For more details on what to monitor and how to monitor it, I'd suggest two books, one free, one not. The free book is the Troubleshooting SQL Server. The not free book is SQL Server Query Performance Tuning.
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