Usually, the parts have names like this

name.z01
name.z02
name.z03
name.zip

1. concatenate the name.zNN files in lexicographical order, followed by the name.zip file

   cat name.z0? name.zip > name-all.zip
   

2. Correct some internal directory structure to reflect the fact that all parts are now in the same file.

   zip -F name-all.zip 
   

   Omitting this step leads to errors:

   $ unzip name-all.zip
   Archive:  name-all.zip
   warning [name-all.zip]:  zipfile claims to be last disk of a multi-part
   archive;
   attempting to process anyway, assuming all parts have been concatenated
   together in order.  Expect "errors" and warnings...true multi-part
   support doesn't exist yet (coming soon).
   warning [name-all.zip]:  12582912 extra bytes at beginning or within zipfile
             (attempting to process anyway)
   file #1:  bad zipfile offset (local header sig):  12582916
   	  (attempting to re-compensate)
   ..
   

3. unpack as usual

   unzip name-all.zip
   

4. It may be that directories do not have the 'x' (executable) bit set:

   find . type d -exec chmod ugo+x \{} \;