A 3rd-Country National without a Permanent Residence Permit needs to have a Work Permit in order to get a job as a regular employee. This is not an easy process. Many papers need to be provided (such as diplomas and certificates) - all translated with apostille. Note that there is a substantial risk nowadays that the labor office refuses the application for a Work Permit, especially now there are so many unemployed already in Czech Republic, and therefore it becomes easier for the Labor office to find a suitable person in Czech Republic.
In order to apply for a Work Permit, the employer needs to initiate the process, then the position is posted for 30 days, and if no suitable person is found, the Work Permit is granted. With that, the 3rd-Country National can then apply for a Visa for work purposes. The total process may take 3-4 months.
If a 3rd-Country National loses his job, then immediately the Work Permit expires and he has 3 days to announce this to the Foreign Police.