Harvest Moon: A Wonderful Life Special Edition

In order for your cow to get pregnant you need to order the Miracle Potion from your ledger. For the standard cow you start with, it'll cost you 2500g. Takakura will apply the potion the next day, and your cow will go through multiple stages of pregnancy until after ~20 days she finally gives birth to her calf.

A cow gives milk for ~35 days before she dries up and needs to give birth in order to produce milk again, so I suggest you try and time the birth of the calf with your 35 days milking period. You can still milk your cow while she's pregnant, you just want to avoid having her dry up, thus losing out on possible money you could have made from the milk.

Hint: If you don't plan on keeping the calf, sell it immediately and keep the Mother's Milk that your cow will give for 5 days until you can cook "Dhibe Cakes". See Construction Worker for more information.