I ordered a Ward Lab kit to test my tap water. When I take the sample should I run it through a water purifier like if I were going to brew, or should I run it straight from the tap into the container?
Depends on what the purifier is. If it is just a carbon filter it doesn't matter as those don't effect the content of any ion that Ward Labs will check (or any other ion, really). If it is, conversely, an RO unit then you should send the water you are going to brew with though there really isn't much point in doing that unless you suspect there is something wrong with the system.