Yes, you can switch from an Employee Card to a Blue Card later, but you’ll have to meet all the Blue Card requirements and basically reapply. Switching the other way around (from Blue to Employee) is rare and usually not worth it.
As for applying — you can start the process at a Czech embassy back home or, if you’re already here, go to the Ministry of Interior. You’ll need things like your application form, biometric data (fingerprints, etc.), work contract, proof of where you’re staying, your financials, and a clean criminal record.