On this page of the Disco Elysium game guide, you will find a detailed walkthrough of the Find booze and drink it task.
In Disco Elysium, the task Find booze and drink it isn't complicated - simply acquire a bottle of alcohol (such as beer, wine or vodka) by any means of your choice, then have Harry drink it.
A variety of alcohol types can be purchased, for example, at the Frittte kiosk. Place an alcohol bottle into Harry's hand (left or right). Next, select the dialog options to have him look at the bottle, then prompt him to open it and take a sip.
Drinking alcohol will result in Harrier immediately losing 1 morale point, so make sure beforehand that he won't die as a result.