Quite poor and disjointed when compared to other major powers of the time like the French Republic or German Empire. The United States had only utilized conscription from its population to bolster its military in wartime once before (during the Civil War; executed questionably), and the Army existed in a nearly-dismantled state in peacetime, with the largest permanent unit being the regiment. State militias or volunteers called by the President, in theory, would form a majority of the Army's strength when it went to war.

U.S. Military Personnel on Active Duty on June 30 of Each Year, 1895-1905

Year	Army	Navy	Marine Corps
1895	27,495	11,846	2,885
1896	27,375	12,088	2,217
1897	27,865	11,985	3,806
1898	209,714	22,492	3,579
1899	80,670	16,354	3,142
1900	101,713	18,796	5,414
1901	85,557	20,900	5,865
1902	81,275	23,648	6,222
1903	69,595	29,790	6,658
1904	70,387	32,158	7,584
1905	67,526	33,764	7,011

The War Department was divided into bureaus, whose heads, or chiefs, reported to the Secretary of War. Those that existed by 1890 were;

• Judge Advocate General's Department

• Inspector General's Department

• Adjutant General's Department

• Quartermaster Department

• Subsistence Department

• Pay Department

• Medical Department

• Corps of Engineers

• Ordnance Department

• Signal Corps

The highest officer in the Army was the Commanding General, but he exercised relatively little control over the actual function of the service, and was a "commander" pretty much in name only. He enforced orders relating to military operations, control, or discipline from the President or Secretary of War, but did not control fiscal, supply, payment, and recruitment affairs, which were conducted through the Secretary of War and the respective bureau chiefs. The chiefs acted independently on their issues of interest, but often clashed with each other and the Commanding General, leading to inefficiency, if not outright incompetence. The bureau chiefs also formed a General Staff, but it was not like a "general staff" in a strategic sense. This led to great problems during the Spanish-American War. I previously made a post about the structure of the Army from the 1800s to 1940 which covers these problems and the way they were solved in relatively short order here, but I will repeat it below since it basically dovetails with what I've written above and contains much relevant information.

Sources:

Department of Defense Select Manpower Statistics, Fiscal Year 1997

Hewes, James E. United States Army Special Studies, From Root to MacNamara: Army Organization and Administration. Washington: United States Army Center of Military History, 1975.

We actually talked about this in my American Foreign Policy class.

Basically, your question addresses the same time period as the Spanish-American War. This war proved that American military infrastructure was drastically in need of change.

The war began Spring 1898 and lasted until August 1898, with the United States being victorious due to low Spanish morale in Cuba (due to decades of Cuban resistance) and the Philippines.

The army itself was unprepared. Following the Civil War, the country underwent massive demilitarization. There was a small regular army, and then each state had its own army that responded to their state governor, meaning that each army had their own standards of preparedness and guidelines. This would change after the Spanish-American under the Dick Act (1903). This nationalized the military standard and followed the precedent set by the state of New York.

Domestic transportation was a major issue within the context of this particular war.There were only three modern battleships at this time—one of which, the U.S.S. Oregon was in China. This limited transportation ability to get to the Cuban Island. The other battleship involved was the U.S.S. Maine, which was blown up on a diplomatic mission. The explosion of this battleship may or may have not been caused by the Spanish, but that’s another discussion. Also, there was only one railroad that went down to the port in Tampa (the closest one to Cuba).

Equipment discrepancies and numbers were a factor as well. The wartime army during the course of this war were pulling from the National Guard in order to have enough forces. They were getting the cheapest and most outdated weaponry the United States could muster up. The Army branch itself were getting German weaponry.

In short—transportation, numbers, and equipment were severely lacking during this war. This forced the United States to really look at modernizing it’s Army/military at the turn of the century. They looked to European powers for inspiration (mostly France and Germany, who boasted the two largest land armies at the time).

The Army adopted a draft army following the Spanish-American war as well, which had been heavily debated for a while now. As seen during the war, the United States did not have the numbers they needed to fight in a war and couldn’t afford to wait for volunteers in case they needed quick mobilization.

This is all I can write up for now, maybe I’ll edit it later.

(This is my first post in AskHistorians, so if there’s any violation, sorry! I had fun writing this up. I know there’s a strict policy here. I hope it’s alright.)