What you mean by id card ? is that permanent residence that you are meaning ?, to apply permanent residence you must stay here 5 years in advance. if you completed 5 years staying in Slovakia you can apply Permanent residence, This law will apply only if you are coming from outside EU.
The main thing you have to do is to procure a temporary residence permit.All important you´ll find on this page: mic.iom.sk/en/residence/temporary-residence/21-ziadost-o-prechodny-pobyt.
Articles to help you in your expat project in Bratislava