Highly recommend scheduling 1 hour sessions every 2 weeks way in advance at a time in the diary of the coachee that is a good time - preferably not straight after their hard meetings and preferably not when they are most needed by their team members or managers for important things. Change takes concentration, focus and commitment - as coach you can't control these but you can be skilful in making them more possible.
I generally give my 1-3 minute intro, and ask the coachee to do the same, picking up on common career moments, or outside interests, or phrases or - whatever catches my attention. And then start to ask questions around those things, ensuring as I do that the coachee relaxes. If the coachee does not relax, there is always a next time to try again. While coaching is not counselling, deep relationships are still established and must be done sensitively and sensibly.
I take notes especially of things I can do outside the meeting to help - for instance referals to other people, books or websites. Towards the end of the meeting I setup a working agreement/plan about what I will do for the next meeting, and what the coachee will do eg meet someone, read a web site. In the early days the "homework" I give is usually short and used as basis for conversation in the followup 1-1 meeting.
I like to summarise the meeting in an email, especially what I have to do and by when, and what the coachee has to do and by when. For some coachees, this might be the opportunity to complete an Myers-Briggs for me/them (see Free online Myers-Briggs Type Indicator).
The way I create these summaries is important and simple. After every meeting, I summarise in email by forwarding the previous emailed summary. This creates a rolling log that is extremely easy to manage, always backed up by email servers, and a simple format to check progress - dates, timeline sequence, agreements, what was done, what was not done, etc very easy, and I've successfully used weekly rolling logs in this way for over a year. But this does not replace my low-fi notepad and pen for during the meeting - I sometimes also end up drawing things!
I do my "homework" (or actions if you prefer such speak). This begins to form the basis of trust for someone who does not know me - I do what I say, repeat, repeat. And I hope that the coachee is also doing their "homework". Sometimes I drop-in and check if I can help to ensure that the actions are being done - especially in cases where progress is slow or non-existent. I like to discover what in the workplace could be blocking the coachee - in order to strategise to unblock progress.
The 2nd 1-1 about 2 weeks later. It usually goes a lot smoother as the ice is broken and there is progress to report on both sides, and some homework to specifically discuss and put effort into. Or, there is no progress and this too is something to specifically discuss and decide to put further effort into or not. In opt-in engagements, people opt-in by doing, and they opt-out by not doing. There is no right or wrong as it is all about what can be done with the time and effort allowed.
I like to hear about what work problems were encountered since the previous 1-1. What they thought about the homework, what questions they have now for me. Then I like to clarify and rephrase my understanding. If there is homework output/outcomes then we discuss that for a bit (helps to know a lot more about the homework you've given in order to have a fruitful and enlightening discussion!).
During all this talking, again I am making notes like in the first meeting. And I am checking each item on the agreement list of what the coachee achieved, and what I achieved. Usually this cycle results in a couple more actions for both of us, and then I request the next piece of homework....
And this essentially is how I use 1-1's. They're status meetings, repeated, to enable shared understanding and for me to offer help as well as point in the direction of useful things as homework for the coachee. This inevitably creates more work for both of us - just enough for us to do in the 2 weeks inbetween.
If the homework is too much, then it is not completed - for either of us.
If the meeting is too long, then summarising it is too hard - try to always leave wanting more!
If there is no progress, and it seems like there won't be before the next session, decide together to stop sessions until there is enough slack time again for the coachee to continue their growth plan
For extra depth in getting 1-1's right, I also highly recommend Stephen R Covey's The 7 Habits of Highly Effective People.