Well, in some ways you just have to ask yourself the same questions you should be asking yourself as an employee, just there will be different answers.
But the one dominating thing is that as a consultant you are usually being paid to solve a problem, as opposed to perform an activity. In the mind of whoever is paying you, they had a problem and they brought you in to solve that problem and they want it to go away, preferably with the minimum of supervision or drain on their time.
As a consequence, expectation management is a huge thing - it is very common that the problem you are there to fix may not have been understood well and so expectations are unreasonable, if not unachievable.
This also means that it is also very common, as a way of managing expectations, that the first part of the consulting is to write your own scope.
This allows a crucial aspect to be defined, being "when have I finished or succeeded", because you and they may well have different ideas about this otherwise.
As a consultant, if you look for repeat work or good referrals, you need to be trying to show that you are delivering service and value every hour you are billing. If you can do that they will happily pay whatever rate you charge. Don't hang around and "milk it". For some reason most people value a dollar paid to a consultant far more highly than one paid to an employee, so demonstrate you are worth it.
I usually like to create a "Project
Execution Plan" as part of the offer, or worst case at the kick-off meeting. This can be as simple as one page that details the scope, duration, deliverables, who and how you report to, expected location and times of performing the work, and so on, signed off on by the client. This creates a referable basis that creates common expectations, thus greatly reducing the possibility of conflict.
I've been consulting as an engineer for 30 years now and had to learn as I went.
But every situation is different, you just have to wing it sometimes.