With a few exceptions (Fort Sumter being the most obvious), forts and outposts that fell within the boundaries of the seceded states were taken without too much trouble and few if any casualties. It varied from region to region, but sometimes the Federal troops (sometimes just militia) simply cleared out, knowing that they were hopelessly outnumbered and unlikely to get any kind of reinforcement. The states that voted to secede weren't shy or quiet about their intentions, so the soldiers in the forts/outposts often had plenty of time to gauge what the likely outcome in their area would be, and prepared appropriately for a timely exodus (usually with every piece of ordinance from that fort/outpost that could be carried, hitched, or hauled with them).
Naturally, some stuff was left behind, like fixed cannon or half-built ships in boatyards. The Confederates took advantage of each such instance, and scrounged every scrap of materiel they could lay their hands on. The Federal officers often burned or spiked the materiel and guns they had to leave behind, but some stuff was indeed salvaged.
As for the troops themselves, there was usually a formal offer of surrender if they were still at their posts by the time the southern states seceded, and put a unit together to challenge the fort. In some cases, Federal commanders consolidated all their forces from nearby forts into one strong one (like Fort Pickens, in Florida, which actually held). Again, though, in lots of cases, a cursory and spirited attack would often drive the defenders out, and the forts would be taken without too much trouble (see Fort Morgan in Alabama). Remember, this would have happened in early 1861, before either side had really consolidated their forces or trained up their soldiers, so discipline and fighting know-how was in short supply.
[Sources: Bruce Catton, 'Grant Moves West'; Shelby Foote, 'The Civil War, A Narrative, vol. 1']
In general, posts in the seceding states were taken over by state and local militias who forced their surrender. Many commanders had ties to southern states or believed that local authorities had the legal right to the arms and other equipment within posts in their state. The soldiers within those posts who remained loyal to the national government were paroled north and many went on to fight in the ensuing war.
Now, let's look at some examples. In Texas, the Department of Texas was led by Brevet Maj. Gen. David E. Twiggs. He was a Georgia man but had served the United States through three wars. He opposed South Carolina's nullification movement in 1832 but in 1861 had a different mindset. That mindset wasn't unknown to the War Department, which in early Feb. 1861 had ordered him relieved of command. Unfortunately, the order arrived too late.
In mid-February, Twiggs surrendered all federal posts in Texas. Under the terms of the surrender, the 2,600 soldiers in Texas ─ about 15 percent of the U.S. Army ─ were permitted to keep their small arms and were assured of safe passage to the Union. Twiggs received a hero's welcome in New Orleans and was named a major general in the Confederate Army.
Unfortunately for the U.S. soldiers in West Texas, news of Fort Sumter arrived before they left the state. About half remained, and 800 of those were en route to Indianola, a coastal town, where they expected to meet transports to take them out of the state. Brevet Lt. Col. Isaac Reeve commanded many of the rest, a party of 336. In early May, they were met by 1,500 Texans and six cannon. Faced with this overwhelming force, they surrendered.
Over the ensuing 15 months, the group's officers accepted parole and headed north. There are various accounts of the other soldiers' confinement, which contemporary accounts say included heavy labor, scanty supplies and occasional imprisonment. On Feb. 25, 1863, the 278 soldiers still in custody were freed via a prisoner exchange.
For this account, I suggest Robert Wooster's Frontier Crossroads: Fort Davis and the West.
Across the South, arsenals, lighthouses and isolated forts were surrendered without incident. Their inhabitants were transferred north or to steamships at the coast, generally speedy and without incident, except in the aforementioned case of Texas.
Now, there were four exceptions to this general pattern of turnover. One you already know: Fort Sumter, in Charleston Harbor. The other three are all in Florida: Fort Zachary Taylor in Key West (that city was to remain in Union hands throughout the war); Fort Jefferson in the Dry Tortugas west of Key West (an incredible achievement of engineering and logistics, it's well worth a visit if you get the chance); and Fort Pickens, at the coast outside Pensacola.
I'm going to talk about Fort Pickens, because forts Jefferson and Taylor didn't see combat, and you know the story of Fort Sumter.
When 1861 began, Fort Pickens was empty. Like Sumter, it was situated at the entrance to an important harbor. Unlike Sumter, it wasn't surrounded by hostile batteries. It could come under fire from other positions, but its position was not as dire as that of Sumter. When Florida succeeded, Pickens was under the command of Lt. Adam Slemmer, who had all of 40 artillerymen to defend his post.
State militiamen seized the military posts in Pensacola, but Slemmer escaped with his men (and a few more, from the Navy yard in Pensacola) to Fort Pickens. On Jan. 12, Floridian officials demanded the surrender of the fort, but Slemmer refused even though he knew he couldn't defend the fort very well ─ if at all.
President Buchanan cut a deal with Florida U.S. Sen. Stephen Mallory (a secessionist and future Confederate Secretary of the Navy) in March. Under that deal, the North would not reinforce Pickens and the South would not attack it. Despite this deal, the navy sent the USS Brooklyn to Pickens and anchored it within cannon shot of Fort Pickens. Aboard was a company of soldiers to defend the fort.
With Lincoln in office, plans changed, and there was a new determination to reinforce and hold Pickens. At the same time, Braxton Bragg had taken command of the Confederate forces in Pensacola, and there was a danger that an attack could come at any moment. Unlike at Sumter, Lincoln's administration acted decisively ─ By the end of April, there were 1,100 soldiers ashore at Pickens, which would remain in Union hands from the start of the war to its end.
The first thing to remember about the Pre-War US Army was that it was extremely small, less than 20,000 strong, and most of those forces were deployed in the west. More troops were deployed to the north, along the US-Canada border. The only formations which really existed in the south were the garrisons of several forts protecting southern harbors. Among the Army men, many of the officers resigned to serve with the Confederate forces, but few enlisted men resigned (Ive read estimates as few as one, but Ive never seen much consistency). That left the garrisons of southern forts relatively intact, in locations like Fort Monroe, Fort Sumter, and Fort Pickens. Some of those locations were abandoned when their commanders declared their position untenable. These tiny garrisons were either concentrated in defensible locations, as in Charleston when the Federal garrisons of the harbor concentrated at Fort Sumter. The other forces made their way north and began to form the core of the Union's defenses.
At the fortresses deemed defensible, a standoff occurred between secessionist officials who wanted to take possession of the forts, and the officers who refused to surrender them. This drama famously played out at Fort Sumter, where the garrison refused to surrender and was eventually forced to surrender their position. At other places, like Fort Pickens and Fort Monroe, the Union navy was able to effectively reinforce and resupply the forts.
So to summarize, most the the rank and file of the US Army was deployed outside the Confederacy, and the small garrisons which were in the south left largely intact. Until Fort Sumter, the Confederacy and the Union existed in a state of Quasi-war, in which both parties were hostile, but neither wanted to make the first move. In this period, the Union garrisons went unmolested, which allowed Buchanan and Lincoln the leeway needed to extract vulnerable forces and reinforce strategic locations.
Source:
Russel Weigley, A Great Civil War