There are many books that impart basic saṁskr̥it skills. A good modern set of books is the teach yourself saṁskr̥it (dīkṣhā) books. Dr. Narasinga Rao goes through every page of these books in his youtube classes.
- prathama dīkṣhā books
- prathama dīkṣhā class recordings by Dr D Narasinga Rao
- pañchatantra class recordings by Dr D Narasinga Rao
- vyoma labs class recordings on many kāvyas etc
A basic knowledge of vyākaraṇa is useful (and necessary), as captured in the dictum `काणादं पाणिनीयं च सर्वशास्त्रोपकारकं’. There are many books and classes which cover the laghu siddhānta kaumudī in some detail.