How easy was it to join the Communist Party of the Soviet Union, and how common was raising in the ranks from a low level? Additionally, how was loyalty to Marxism Leninism guaranteed, and why was it largely unsuccessful?

I am currently reading Sheila Fitzpatrick's Everyday Stalinism which goes into some detail about this. However she focuses exclusively on the Stalinist era during the 1930s, so my response will primarily focus on this time.

In short: it wasnt easy. You could apply to be a member of the Communist Party, but not often would you be accepted. The admissions process involves a complicated series of background checks, involving letters of reference from existing Communist Party members, investigations of social status, cross-examinations for political literacy and knowledge of Marxism-Leninism etc. In short you had a proven track record of being faithful to the Revolution. This had an effect of course admitting in the devoted, but the admissions procedures were often highly biased in of themselves. Those with a poor worker or a peasants background were more often preferred than those with white collar or professional background.These same standards also applied to the communist youth group Komsomol. And suffice to say, with you came from a bourgeoisie background or was ex-clergy, your chances of admission would be close to nil. Many sincerely devoted communists actually expressed frustration at being unable to join.

Advancement up the rung was probably a mixture of being able to pull the right strings as well as industriousness and devotion. Currying favour with the other higher ranking Party members certainly helped. Oftentimes one of the requirements was that you actually believed in the system.

In the aftermath of the Purges, they lowered admission standards to fill in their losses and more people from white collar backgrounds could finally join, in a way improving the efficiency of the system.