1. The DNC and their members are generally ignorant of good security policy and had an easily hacked system.
2. Some Russian intelligence agency hacked the DNC's email servers.
3. A bunch of other people/hackers/groups hacked the DNC's email servers, as it was "left out in the open", so to speak, and was a trivial target..
4. One group at least used trivial methods to do so and left behind evidence.
5. The FBI/NSA//DHS/etc found that evidence.
6. One of these hackers passed information to WikiLeaks. WikiLeaks has denied that it was Russians who did this.
7. The FBI/CIA claim that the Russians hacked the DNC servers.
8. The press and political opportunists jump to the conclusion that it was the Russians who released this information to Wikileaks.
9. The FBI/CIA classified what they found and aren't going to put it in a press release.