This is a question that people have written books about, so there's not a very simple answer here. I've read a decent amount on this subject, though I'm not a historian, so I'd ask for people to correct me.
In February of 1917, the Tsar was overthrown and was replaced by a provisional government. Why was he overthrown? Well, there are lots of answers to do with how hard life was, what a terrible ruler he was, and whatnot, but my understanding is that it really boils down to two things.
First, World War I was going absolutely terribly, and the troops were basically revolting. The Brusilov Offensive of 1916 had made some progress and improved morale somewhat, but had gotten bogged down and eventually stopped. And the troops were not only dissatisfied, but they were political and becoming radicalized against the Tsar.
Secondly, the winter of 1916-197 was brutal. Absolutely brutal. It was freezing beyond belief and people were suffering badly. This wasn't just in Russia - this winter was referred to in Germany as "Turnip Winter", as the population turned to Turnips to survive.
Basically, all this boiled over in February 1917. The people marched on the Winter Palace in St. Petersburg and took it over. Meanwhile the Tsar, who wasn't in St. Petersburg but was closer to the front with the troops, was basically told "you need to step aside, as the troops won't protect you and won't put down the revolution". So he did.
So in steps this provisional government, headed by a liberal noble named Georgy Lvov. So why did this fail? Again, I can think of 2 big reasons:
First, after coming to power, the provisional government found it absolutely essential to stay in the war. Seems odd, right? This revolution which swept them into power on the backs of an anti-war uprising, and they stay in the war? There were several factors here. One was that the noblemen who were put in charge of the government genuinely felt an obligation to their allies. They didn't want to lose the war; they thought they could do better than the Tsar and his incompetent government. Secondly, having just changed their government, they needed to maintain credibility and support with their allied countries. The worst thing they could have done was pull out of the war, breaking their promises to their allies to keep fighting, and thereby be isolated in the world. Lastly, the costs of peace would have been immense. Germany wasn't just going to stop fighting - you'd need a treaty. And Germany's demand for peace were insane (as you'll see soon).
Second, the provisional government never got their act together. They had these grand ideas about how to make their government permanent (as opposed to provisional). After all, this provisional government didn't have much legitimacy. How to get legitimacy? Why, elections! Democracy! All these enlightened nobles had the bright idea of creating a national legislative assembly (similar to the French in 1789). The problem was they took forever in organizing these elections. Russia had never had elections, so everything had to be decided. Who could vote? How to vote? How many representatives? How to draw districts? All this stuff. And they took forever to actually figure out how to do this stuff. Their goal, noble as it was, was to be the most democratic and egalitarian government ever. But they took too long.
To cut a long story short, after a few months of this, the people got restless again. There was an uprising in July (the July Days) which didn't work to undo the government, but it did enough to get Lvov out of power. For the next few months there were various power struggles with people like Alexander Kerensky and Lavr Kornilov. Eventually, the provisional government sort of...ran out of steam. They had no institutional strength, no popular support and no backing from the army. In October, the Bolsheviks kicked down the door of the Duma and told everyone to get the hell out. They took over.
As a little postscript, the Bolsheviks basically took the two problems of the provisional government and just...solved them. They were fervently anti-war, so they went to the Germans and said "we want to end this war, what do you need?" The Bolsheviks eventually agreed to sign the Treaty of Brest-Litovsk, a ridiculously punitive treaty. If you google the treaty and do an image search, you can understand why the provisional government would never agree to it - it's insane how much the Bolsheviks surrendered to the Germans. But the Bolsheviks wanted to end the war at all costs, so they signed it. Eventually the Allied Powers (the US, France, Italy, England) forced the Germans to renounce the treaty, and the USSR got the land back. But it wasn't because of their own doing. Not really.
As to being feckless...well, the Bolsheviks were not feckless. While this is getting too lengthy, the Bolsheviks got shit done. At least at the start. Lenin was not timid. And while he had to fight a brutal civil war to maintain power, he won, and the Bolsheviks controlled Russia.
Hope that helps.
Sources
A People's Tragedy, Orlando Figes
Revolutionary Russia, 1891-1991, Orlando Figes
Paris 1919, Margaret McMillan
A World Undone, G.J. Meyer
Nicholas and Alexandra, Robert K. Massie