Clause 6 is about planning. Planning includes actions to manage risks and opportunities (6.1) and second (6.2) set objectives and plans to realize those. Besides these day-to-day operational planning aspects, planning changes is included as (6.3) in the planning section and refers to changes of the management system.
There are many different ways to proof compliance with planning when you are being audited. Certain applications or software can be very helpful with planning daily operations, or manage projects, but that type of planning is not required here. This clause forces you to think about the things that you are currently not doing yet. Either to improve operations, or to avoid undesired outcomes of any kind.
With simple excel sheets you can create your risk and opportunity prioritization matrix for example, but a wide range of software and other tools are available as well. A useful aspect of planning matrices for risk and opportunity management would be a manner to prioritize possible actions. Typical filters are urgency, costs, implementation time and weighted impact factors.
Other tools such as the Affinity Diagram to organize suggested risks and opportunities or the Activity Network Diagram to determine the critical path to reach set objectives can help you planning actions ahead to improve your organization.