Generally the Shimano brifter is not servicable because you cannot get any parts for it. Sometimes tho the cable breaks off, or you crash and it gets full of dirt, or it has been sitting up for a long time and the grease has gummed it up. It could be made to work if you could get it apart and back together. Well, it can be done if you pay attention to where all the parts go. You only need two special tools:
The one on the left is a roll pin that is used to hold the brake return spring in place. It is also very handy for reinstalling the spring that returns the large blade. The tool on the right is for the castled nut that holds the pivot on the back of the blade. You will also need the usual tools and a dental pick or a spoke.
The key is laying the parts out so you can put them back in the correct order.(The picture below shows how to not lay it out)
There are really only two sticking points. One is the return spring for the large blade(left side in pic). I found that the roll pin is perfect for holding it in place while you reinstall the blade. It is also easier to put the blade in a vice and then insert the ratchet assembly(bottom right). The other tricky part is installing the assembly of the small blade(top right). It has a ratchet on it that needs to pass by the body of the ratchet assembly. You can hold it back with a paper clip but I find that it will catch on the return spring for the small blade. Once it is installed you can push it off the spring with a pick. It is not to hard. This shifter had been in a crash. It hardly got a scratch on it but it was full of sand and would not operate at all.