This is when you find all the bugs that you were too lazy to check for when you "thoroughly" tested the system before you installed it!

Ensure that you prioritise the problems, especially if things seem to be going badly wrong. Be specific and set the priorities for the whole business, not just your part! Communicate these priorities clearly to the supplier.

Keep a log of the defects you have found. One really effective way is to use email- send one email to the software company for each bug that you find, but send a copy to a special email account. When you are happy that the problem has been found, archive the email from the special account. This way you can be sure which problems are remaining and you also have a legal record of what you told the company...

Any bug report should state clearly how to make the fault happen- just like when you take your car to the garage, a complaint of "it doesn't work properly" isn't much use.

Try not to send duplicate bug reports- one clear reproducible example is all that is usually enough.