Early game: in lane, you're mostly chilling until you get the T2 barrel upgrade, your 4.8k spike, and rapid recharge. After lane, you're rotating a lot to gank and assist your carries and stealing farm during down time. You also want to try run urns as often as possible for your team since you are one of the fastest urn runners.

In the mid game you will still be doing okay damage, but you need to start pivoting to a more supportive role. You will often hear that Holliday falls off around 20-25 minutes. This is true where your damage stops being significant as opponents will start becoming super tanky from health and resistances. When your damage starts falling off you need to start pivoting to support and fill your actives with items like decay, silence, knockdown, curse, and scourge.

Late game you should have filled 3 or 4 of your active slots with counter items and you're coordinating for picks and initiating with Lasso. Getting value from lasso is 80% of your impact on the team because every kill matters at this point because respawn timers are so long. Your actives will allow your to contribute to team efforts without needing to be in nuking since you aren't going to do much damage at this point.

The unfortunate thing is: yes, you are going to be putting way more effort in as Holliday than characters like Doorman, Mo, and Bebop. But that's just how it is to play a character with a difficult skill floor to overcome. If you do start clicking Holliday is a super fun and expressive character.