First things first, can you supply data sheet links to the load cells. It sounds like you have an industrial design task, your cells may already have conditioned outputs. If this is the case, your design task is easy, you'll just need to read the outputs (digital or analog) into a pretty vanilla sort of micro circuit/logging cct. You may be able to get away with off the shelf equipment.
We'll need to know more to advise.
If you are reading them raw, you'll need a more elaborate cct as Jon has suggested. There the issue of reading Whetstone bridge which can be done by an 'instrumentation' amplifier (google this type) but also balancing, zeroing and temperature compensation. All doable....but we need more information to help.
Lastly we'll need some sort of idea of the accuracy and sample rate. High sample rates will require lots of memory (if you are storing it in a separate circuit) or a high bandwidth data connection to a computer to store it. High accuracy will require lots of attention to detail on the load cell construction, the wiring lengths, temperature sensors all the way to even how you solder the wires together. Low accuracy and you can simplify things a fair bit.
As a start, assuming a raw Whetstone bridge, I've used an AD8555 and AD623 instrumentation chips for low accuracy applications. Read the data sheets and app notes for these to get an idea on what your requirements are and post back once you've got a bit of a handle.