If you are on probation for 1 year and have a conditional discharge does that go on your criminal record?

If you're asking in the US then technically you don't have a criminal record. In other words, you don't have any record of conviction. What employers may see once you've been discharged is the charges that were brought against you and that they were dismissed. Also, you still have an arrest record. You can honestly answer "no" to "have you ever been convicted" but if they ask "have you ever been charged or plead guilty/no contest..." you have to be honest but explain that they were dismissed.