Building a PC from components is easy enough. There are only a handful of basic components & they simply slot together. Care needs to be taken to avoid static discharge when handing components such as CPUs & memory. As to whether you could reuse parts of the old PC, it would depend upon who built it. Some brands (e.g. DELL) in the past have used proprietary motherboards, power supplies, connectors & cases making them more difficult to swap major components.
Someone experienced could probably assemble a PC from scratch in 30-40 mins, loading the software would take a lot longer, several hours depending upon what you wanted installing.
Assembling a PC from components may not save you much money vs buying a new one but might lead to greater self-satisfaction. There are plenty of companies that will build PCs for you, or you might be lucky & pick up a bargain 'factory refurbished PC' from a mainstream supplier like DELL, Lenovo etc. I recently purchased a £480 DELL refurb system unit based upon a 3.6ghz Intel i7 with a 500gb HDD, 8gb memory and Win 8.1 for less than it would have cost me to purchase the component parts. At the same time I built a 'headless' mini-ITX based USFF system to act as a data-logger for a weather station for £200 reusing memory & SSD I already had.
My advice would be decide what you want it for & arrive at a specification, make a shopping list of components & then price up a DIY PC vs one off the shelf.