When we speak quickly, we subconsciously make small changes to our speech to make things easier to say. In Sanskrit, these subconscious changes are written down. Collectively, these changes are called sandhi.
Here are some examples of what sandhi can do. In each example, the left side is how a word might appear without sandhi, and the words on the right are how the original word might change due to sandhi:
saṃjayaḥ ⟶ saṃjayaś, saṃjayas, saṃjayo, saṃjaya
hariṇī ⟶ hariṇy
gṛhe ⟶ gṛha
etam ⟶ etaṃ
etat ⟶ etac, etaj, etad, etan, etal
Sandhi can be acquired by just reading or listening to a lot of Sanskrit. It also helps to read out loud and notice how your tongue moves from sound to sound.