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I would recommend doing some reading first. Here are some good resources:
- Forensic analysis (OWASP)
- Computer Security Incident Handling Guide (NIST)
- (Read this and tell me if it reminds you of what some software you use does to prevent attacks, he he!)
- Unhacking your site (AkeebaBackup.com)

Analysing a hack is not very easy and it's almost impossible to detect if it was a "back door hack", i.e. another hosting account modified your site's files due to a bad ownership/permissions configuration. The reason being that back door attacks would only show on the other site's logs or the bash log file (in case the attacker used ssh on a compromised account) which is simply not accessible to you.

Furthermore, if someone stole your FTP/SFTP or your database access credentials, it's very unlikely that you can gather adequate information. That would require access to FTP, bash or MySQL logs which may not be even kept on a cheap shared host and, certainly, are not available to you.

However, the most common hacking reasons being web-based attacks and permissions issues, I think that you can figure out which one of those two venues was used in an attack and protect your site against it accordingly.