Project Management does what it says - manages a project, hopefully in an effective and efficient manner.
A project is defined as a temporary initiative or intervention, with a specific outcome or target and within time and budgetary constraints. You may have come across various methods of project management, such as PRINCE2™, Agile, etc. These are more or less formulated - some a general approach, others with specific properties and characteristics. As an example, you can combine PRINCE2 and ITIL® - white paper available to download on this link.
What matters is that you adopt some framework to help you manage the HR project, or at least delegate to someone else and be able to know if they are keeping to a required schedule and/or budget, and if not, why not.
There is various software available to help you with project management. The most well known is probably Microsoft Project. It's sophisticated software and if you learn how to use it - and need all its functionality - it can be really useful. However, we would recommend you invest in some training first; for example the video training produced by SimonSezIT.com, available through Udemy.com.
There are cheaper alternatives including some Open Source software that is very good, such as Open Project now known as ProjectLibre. Alternatively you can use Excel and still include Gantt charts which help you visually track progress.
For a brief introduction to PRINCE2™ which is widely used in the UK for government funded projects, see our one page summary. We are Registered Practitioners in PRINCE2 and Certified for PRINCE2 Agile. It is possible and often preferable to use some features of PRINCE2 which are appropriate for a smaller HR project - download this article for an introduction.