It depends on multiple factors. When it comes to my favourite genre, I noticed that I can't enjoy dramas all about romance. The story must be intriguing, I like a lot of dark and heavy themes. I have been picking dramas based on the description when I randomly come across a drama with a good looking poster, so I read the description and the reviews and decide if it's going to be interesting.
However, when I looked back at all the dramas I liked, I noticed they were mostly: Law, Tragedy, Melodrama, Action, Suspense, Mystery, and Thriller. A lot of dramas I loved also had little to no romance in it. So I realised I liked interesting, complex, and fast paced dramas with nice male leads that face many challenges they overcome. Therefore, I started looking for dramas like this, as well as asking for recommendation.
Another factor is my mood, so I search the tags or look at recommendations. At times, I want something lighthearted and funny, so I look for those things and watch dramas, such as Wok of Love. Other times I want something heavy, that will make me empathise and cry, such as Missing You, and I look up similar dramas or search the similar tags. Some times I want fast paced action with a lot of fighting, while other times I want a good mystery drama that would simulate my brain. So I look at tags around that.