I'm not a historian at all, but I have done some digging in Google Books. Here's a source from 1874 detailing the military funeral procedures in the United States:

420 If the remains of a flag officer of the Navy or a general officer are brought ashore in the vicinity of a military post the flag will be displayed at halfstaff and minute guns will be fired as the procession moves The number of guns will be that to which the officer was entitled as a salute

421 During the funeral at or near a military post of a civil functionary who was entitled to a salute the flag is displayed at halfstaff and minute guns are fired The number of guns will be that to which the functionary was entitled as a salute

422 On the death of an officer at a military post the flag is displayed at halfstaff and so remains between reveille and retreat until the last salvo or volley is fired over the grave or if the remains are not interred at the post until they are removed therefrom

423 During the funeral of an enlisted man at a military post the flag is displayed at halfstaff It is hoisted to the top after the final volley or gun Is fired or after the remains are taken from the post The same honors are paid on the occasion of the funeral of a retired enlisted man

424 All military posts in sight of each other display their flags at halfstaff upon the occasion of one doing so The same rule is observed toward all vessels of war

425 When the flag is displayed at halfstaff it is lowered to that position from the top of the staff It is afterwards hoisted to the top before it is finally lowered

426 The funeral escort of the Secretary of War or General of the Army will consist of a regiment of infantry a squadron of cavalry and a battalion of field artillery of the Assistant Secretary of War or the Lieutenant General a regiment of infantry a squadron of cavalry and a battery of field artillery of a major general a regiment of infantry two troops of cavalry and a battery of field artillery of a brigadier general a regiment of infantry a troop of cavalry and a platoon of field artillery of a colonel a regiment a lieutenant colonel or major a battalion or squadron a captain one company a subaltern a platoon The funeral escort of a general officer or of any other officer either on the active or retired list when the funeral occurs at any other place than a military post or camp will be ordered by the War Department and will be composed of such bodies of troops not exceeding the number prescribed in this paragraph as the interests of the service will permit But in all cases where the funeral ceremonies take place at or in the immediate vicinity of a military post or where the remains are conveyed through a military post en route to the place of burial the above regulation relative to escort will be complied with so far as the strength of the garrison will allow The flag will be at halfstaff while the remains are at or in the immediate vicinity of the post and the department or post commander will give the necessary orders

427 The funeral escort of an officer will be commanded by an officer of the same grade if none such be present by one of the next lower grade available The ceremony is prescribed in the drill regulations

428 The funeral escort of a noncommissioned staff officer will consist of 16 men commanded by a sergeant of a sergeant of 14 men commanded by a sergeant of a corporal of 12 men commanded by a corporal of a private of 8 men commanded by a corporal of an enlisted man of field artillery one section

429 Six pallbearers will be selected as far as practicable from the grade of the deceased

And another here, from 1818, which is a dispatch from a commandant:

The death of Lieutenant Plunkett which the colonel in conjunction with the whole of his officers and men of the regiment most sincerely laments demands that the usual cavalry funeral obsequies should be duly observed in committing his remains to the earth Captain and Adjutant Dudley with the serjeant major and quarter master serjeant will see that every thing be properly arranged and ready to fall in in procession at half past three o clock pm The colonel will direct that a horse be sent to the adjutant's quarter for the necessary purpose

The whole of the officers and men will parade on this occasion and fall in in military funeral order at the same period and in front of the house where the body lies

It is hoped that Colonel Wilson will order the whole of the Red Hussars to attend on this melancholy occasion

Orders for the firing party &c &c the colonel commandant understands will be given in general orders by his excellency the governor at mid day o clock and the dress one in the afternoon at the same hour until further orders

No man of the detachment to appear in the streets after watch setting without special leave first asked for and obtained from the officer commanding his troop and the colonel begs of the captains to grant this indulgence sparingly

It's far easier to find full accounts of the military funerals of very important and/or famous men. Here's one for a Lieutenant General (1824):

From a Correspondent - Sir John Macdonald KCB a Lieutenant General in the Honourable Company's service died in Calcutta on Saturday last aged 76 His remains were interred yesterday evening between five and six o clock attended by his Excellency the Commander in Chief all the General Staff and a large body of Civilians who assembled to pay the last tribute of respect to one of the oldest officers of the Honourable Company's service in India There is something in a military funeral so particulary solemn and impressive that callous indeed must that heart be which can witness unmoved a procession similar to the one it is our melancholy duty to relate and few there are we are sure who return to their homes without experiencing in full force those awful and serious reflections attending so solemn a duty

Every respect which this Government is ever ready to shew to a long life of meritorious public service was evinced in the funeral we witnessed yesterday evening At about a quarter past five o clock the Right Honourable the Governor General's Body Guard with its galloper guns commanded by Captain Sneyd together with all the European troops in Fort William the whole commanded by Lieut Col Vaughan Fort Major were drawn up opposite the residence of the late Sir John Macdonald On the body being brought from the house the funeral party presented arms the trumpets of the Body Guard sounding a funeral dirge the band playing the Venetian Hymn On the coffin being placed in the hearse the party moved off in slow time flanked by thousands of natives many of whom had been partakers in the deceased's charity to the burial place in Park Street During the procession guns were fired from the Fort the trumpets sounded at intervals and the muffled drums beat their solemn rolls until at a proper distance from the gate of the burial ground when the cavalry and infantry halted and were formed into a street through which the corpse was borne On the coffin being laid in the grave the guns of the Body Guard fired 27 rounds and the infantry three vollies ending a ceremony as imposing in appearance as it was awful and solemn in its effect Govt Gaz May 31