"Would I spend this capital if it were my own money?"
If I answer yes, then it is an automatic approval. Examples of this being petty cash expenditures like one-time licenses for software tools, or very-low-cost on-going services (<$50/m).
If I answer no, then I usually have to engage in a conversation with other stakeholders in the business to build an understanding of how the expense will add value to our business over the long term.
What I like to try and do is push all purchasing decisions into the trivial camp if at all feasible. Outsourcing to 3rd parties is the most obvious way to do this. E.g. instead of hosting your own git repositories on your own servers, look at using Git[Hub/Lab] public/enterprise. This can take a $10k+ capex and diffuse it out into a monthly concern that is lightyears easier to account for and change over time. The challenge is making sure that you aren't outsourcing your key value drivers to 3rd parties. Compliance & industry fit are also a consideration here. Developing some things in house can potentially save you a ridiculous amount of money depending on the specific problem you are trying to solve. And, in-house development will ultimately contribute to a far more important basis of value - your company's intellectual property.