Connecting a Leviton light timer w/ 3 way set up

The black wire at the bottom of your diagram is the incoming hot feed and goes to all the switches. If the timer switch has a terminal screw, hook it up to the new switch the same way it was done at the old. If it has a pigtail lead, you'll have to cut the black wire and wirenut both the cut ends with the pigtail from the timer. The blue wire or terminal on the timer goes to the other black wire (the non-doubletap one) going to the single switch, and the white wire or terminal on the timer needs to be connected to the bundle of white neutral wires at the back of the box -- you may need to use a length of scrap white wire as a pigtail for this.

Also, the weirdly wired 4-way switch is really a 3 way switch in disguise, and make sure the single black wire's loose end is capped off with a wirenut.

The black wire that goes to multiple switches should be your hot leg. If the black wire in the back is on the same side (top / bottom) as the wire going from the screw to the other lights this is the line and it will need to be connected to the other switches and your new one or they will no longer work if capped off if that is the case the other wire is the load. The whites are the neutrals when bundled (some times in a switch loop a single white can be hot, they are supposed to be marked but many times they are not).