It's probably wrong to think of Glyndwr having an army, even in the medieval sense. I think it's more a case that he and his principal lieutenants (Rhys Gethin being perhaps the most famous) led relatively small bands into different parts of Wales and co-operated with the locals. Wales (relative to England) was more populous then than now (though of course the absolute numbers were much smaller) and there was significant manpower to muster, including many formidable warriors. Wales and the Marches had long been a source of professional soldiers.
Welsh and English people traded freely, and addition the Welsh often crossed into England to find work, including seasonal labour connected with the harvest. These business relations continued despite the war, and despite, in the case of trading, government attempts at prohibition. Ties of friendship and kinship were common, particularly in the border areas, and loyalties, as I mentioned in an earlier post, were not always straightforward along racial lines.
So rebellion could spring almost anywhere, and in great force, and die away almost as quickly. Those who partook in it were not necessarily distinguishable from peaceful subjects, at least at first sight. The risings focused on economic targets, such as market towns and the estates and other assets (e.g. mills) of the marcher lords and the Crown. The effect was seriously to disrupt judicial sessions (which were primarily a source of income!) and to prevent the collection of rents and other dues. As the devastation progressed, the point was soon reached where even those who were willing to pay were unable to do so. If your farm has been destroyed and your sheep and cattle taken, you simply have no means to pay!
This economic warfare had dire consequences for the incomes of the marcher lords, among whom, it must be remembered, were the King himself and the Prince of Wales. Used to their Welsh estates producing vast revenues, they soon found themselves with little income, if any at all. At the same time it was necessary to garrison their Welsh castles with additional men, and this did not run cheap. Imagine the cost of putting an adequate garrison into Caerphilly Castle, for example, as Constance Despenser was ordered to do in 1403!
By that time most of the castles in Wales were already under some sort of siege, even if only an informal one, which meant that the English lords could not project their power much beyond the castle walls. This meant that Glyndwr's men had effective control of most of the countryside, with obvious results. The garrison of Caernarfon was reduced to sending a woman to Chester to ask assistance, as no man was willing to brave the journey!
Henry IV's tactical response was to send large armies into Wales. In the early months of the revolt the Prince of Wales (future Henry V) destroyed Glyndwr's properties at Glyndyfrdwy and Sycharth. Other objectives of these expeditions were to relieve besieged garrisons and punish rebels. (Many were hanged, drawn and quartered, but many more were pardoned. The policy seems to have been inconsistent.) However, if the first few years of the revolt there was little success. The King seemed to be cursed by unfavourable weather, and achieved relatively little despite his supposed brilliance as a warrior. On one occasion he sacked Strata Florida Abbey because of the supposed pro-Owain attitude of the monks. (In fairness, Owain also sacked religious houses, notably the Bishop of Bangor's palace near modern Llandudno, and all the religious houses of Cardiff bar that of the Grey Friars. This was not a 'clean' war, if ever there is such a thing.)
The result of all this was that by the end of 1404 almost the whole of Wales was under Owain's control, although it must be said that that control was rather tenuous in places.