Solution 1:

As an Intermediate Redstone-er, I'd recommend doing the following:

  1. Convert long Hopper-Lines into Water Stream Ways, example for if you don't understand my terminology on this:

Water Conveyance SystemWater Conveyance System The packed_ice helps to speed up the transport process, as well as preventing itself from melting like normal ice does. An additional note, replacing hoppers with this greatly reduces block-lag, as myth-busted here: Redstone Myth Busting
(I won't go into all the details here...)

  1. If you have two outputs next to each other, that need to be activated at the same time (for the same amount of time, etc.) then use a repeater to input into one of the outputs.
    Reminder: Power is shared with adjacent blocks when a repeater is used!

Two Outputs powered by One InputTwo Outputs powered by One Input

  1. Redstone lighting updates can cause fps-drops: as detailed in the previous hyperlink above, redstone lighting updates can contribute to a 'massive' portion of your fps being 'eaten-up'.
    The solution: lighting the entire circuit with glowstone (or minimising air-pockets between components for optimum light-emission-reduction).

  2. When using clock-circuits, be sure to optimise it's efficiency. So, example: 'Comparator Clock', run the output from beneath/next-to the Comparator-I/O 'wires'.

Increasing Efficiency for Comparator ClocksIncreasing Efficiency for Comparator Clocks

I hope my tips/tricks have helped with your fps-drops. I'm interested to see whether some of my concepts will be incorporated into later projects. :)

Solution 2:

You can improve your performance by easily changing the particle/animation settings in your video settings.

When you are in a village with thousands of torches, each one of those torches have both a smoke and a flame animation. By reducing that setting or removing it entirely you can increase your performance without seriously affecting the gameplay.

Solution 3:

Everything you can easily increase your fps is mostly found the minecraft video settings.

The bigger the screens size, the lower the frame rate. Having MC be in a window will run faster than in full screen.

Fancy vs Fast I always turn it to fast as the first thing I do when I desire more fps. This changes smoothness of lighting and changes non-3D items to sprites, but doesn't really effect the game all that much IMO.

Clouds. Clouds used to be a fps-dropper but not any more, but could still mean the diffrence between 10 and 15 fps.

Don't use super Hi-def texture packs. These can slow down your fps quite a bit.

Optifine? I have heard it increases fps, but I don't have experience with it.