In my experience it is not a good idea to begin by contacting a regimental museum. They do not hold the service records of soldiers, although some do have some useful lists*. Some of the museums are excellent, friendly and helpful. Others are under-staffed and unable to devote much time to your project. You may find the museum very useful once you have discovered the basics of a soldier's career.

*The Guards regiments do have records of their troops.

Many men are mentioned by name in published sources, although if you are just starting out this might be like looking for a needle in a haystack. Local newspapers carried stories of men enlisting (at least in the early days), mentions when they were wounded or killed, and even letters from the soldiers to the Editor. Post-war, many books were published that gave rolls of honour or even whole lists of men who joined up - but only for a relatively few units. Modern researchers have produced great work on, for example, the Pals battalions, local war memorials, etc - but again for only a relatively few units and places. This is an exercise best left until you are much further down the road and in possession of good information about units and dates that were important to Grandad.