As I think I've understand you correct, you've been called to defend some part of the kingdom, not to do battle overseas. I'm also going to assume this is some part in western or central Europe between 11th-early 16th century. I'll give my account of Scandinavia, seeing as it's "my area". I'll then list some sources and end with a bit more continental stuff.
In the Scandinavian conflicts of late 13th and early 14th century, it usually consisted of one army invading another lord. The invading army usually consisted of more professional troops (such as German Mercenaries, of which we have accounts of ~6000 in this particular conflict). The defenders would retreat to their castles, while the attackers would ravage and loot the surrounding hinterlands for supplies. The defenders would then respond by scorching the earth, open diplomatic talks that would go no-where and call up levies from around the realm to alleviate the siege. The minimum armament of the levies goes along the lines of:
The realm was divided into communities that lived along the coastline, fjords or rivers. These would be expected to have one, or more ships depending on the of the size of the community/town. The communities that didn't live close to the coast would mobilize using horses and sleds/carts.
The moral and quality of the defending levy was often quite poor. When matched up against professional troops, the result would often (but not always) end in the peasants massacred or mass rout (Fotevik, Uppsala, Visby, Akershus). It depends on the context of the situation (moral, disease, supplies, etc.).
Sources:
Fairly similar elsewhere in Europe early on. Further south, on the continent, we see it's slightly different as we move into the 14th century. In the low counties (Belgium) we see the city militia wear uniforms depending on their town and were separated according to their guilds, mid 14th century1. Strasbourg militia bannermen probably at the end of 14th century judging by the armour.
As u/SoloToplaneOnly has give you a very good general answer, I will give you a specific example; the defense against Scotland in 1346, the direct end result of which was the pitched battle near Durham, called 'Neville's Cross'.
Typically, the actual soldiers who fought in the English army were raised via a mixture of the feudal levy (a knight, baron, earl, etc being asked to provide men for defense of the realm), the commission of array, and the retinues of the nobility. In 1346, several powerful magnates of the north had be left behind to defend against attack from Scotland, most notably Henry Percy, the Archbishop of York, and Ralph Neville; who you will notice from a cursory glance at the wikipedia page (though my source for this is volume I. of Jonathan Sumption's ''The Hundred Years War: Trial by Battle'') to be the three key commanders.
So, specifics. Say you are a landed knight of Ralph Neville. You are presented with a requirement, based on your personal income, to provide a set number of men. This varied from 100 shillings to 1000 pounds. If your income is 20 pounds a year, you would be required to provide around 30 archers and maybe 5 men at arms, either by hiring them on or using your own 'villeins' from your lands. You would not receive financial reimbursement for this, and from what we know it generally was only really effective when a threat to the realm was widely known; Edward III tried this in recruiting troops for his invasion of Normandy, and I believe managed to get 3,000 men from the entirety of middle and southern England.
What you might be presented, more likely, is a commission of array. This is a signed contract between you and your lord/employer to provide 'x' number of men for 'y' number of days, for 'z' amount of pay. While this might seem less beneficial to the employer, it actually had a lot of nuance to it; your troops would be expected, and if they were not considered fit, they would not be accepted, and you'd be paid less, or the contract void if the gap between actual and contractual was too great.
Naturally, forces made up of commissions of array were of higher quality than the feudal levy, and 1346 is the real start of the decline of traditional feudal vassalage in England; that is, land for military service. If you were a lord being raised via a commission of array, you would go round the local villages, towns and maybe even pop into a city or two, and look for recruits. Men at arms weren't too common, and had a hefty price, but England had plenty of archers, and of exceptionally high quality - the commissions I've seen tend to read like '70 archers, 43 mounted archers, 32 men at arms with 40 attendants and mounts for attendants and men at arms'. You might even give your men some rudimentary training before hand, though this was more 'raw recruits being tested by their older comrades'. This made up the vast majority of English forces heading to France during the Hundred Years War, and had a similar cousin in the French arriere ban, though I'm no expert there, either.
The last, and most potent quality wise, of a medieval lord's means to raise a force was their retinues. Similar to the Angevin mesnie, these were the professional soldiers hired, trained and personally attached to ''you''. Though the numbers fluctuated, Henry of Grossmont had a retinue half as large in times of peace as he did in times of war, the general rules were consistent. These retinues could be tiny, maybe three or four men, or colossal, reaching into the hundreds and occasionally into the thousands. This was where a lot of the men at arms came from, and formed the backbone of the army which fought both at Neville's Cross and at Crecy. Only the best would be taken, and they could be used to contribute to a commission of array; but the more powerful lords would distinguish between those men kept on temporarily in such a commission, and those with a less fixed term of service
My two sources for this are ''Edward III and the Trumph of England'', by Richard William Barber, ''The Hundred Years War. Vol.I: Trial by Battle'' by Jonathan Sumption, and ''The Greatest Knight: The Remarkable Life of William Marshal, The Power Behind Five English Thrones'', by Thomas Asbridge, for a comparison between late Angevin and late Plantagenet feudalism.
Thank you /u/SoloToplaneOnly and /u/Knight117 for your thorough answers! Speaking as an aspiring author it definitely helps for me to better understand the intricacies of raising armies. SoloToplaneOnly mentioned a difference between defense of the realm and campaigning overseas; what difference would there be in terms of former versus latter? Merely a difference in the number of men raised? Also, in either case, how would this army be internally structured once assembled? I know in terms of medieval armies each person calling their vassals to arms would provide some rough structure to it all, but if a Lord's levy was, say, a hundred axemen, three hundred archers, and fifty mounted men at arms, how would these commands be parceled out? Would they all stay with their Lord or would they be divided up according to 'soldier class', e.g. were cavalry from all levies placed under the command of one designated person in the army, or would each band stay with the Lord to whom they owe their allegiance? Same with archers, infantry, etc.
