For the people living in Ukraine who want to come to Slovakia, there are currently 3 border crossings: Ubľa, Vyšné Nemecké and Veľké Slemence.
Slovakia has set up the so-called hotspots at the border crossings and in some municipalities to speed up the administrative process that needs to be completed upon entering the country.
You can get current information about the waiting times at different border crossings here:
https://www.aid4ukr.com/get-help/waiting-times-at-the-borders-of-ukraine
As Ukraine has announced mobilisation, Ukrainian men aged 18-60 are not entering Slovakia.
More info at https://www.ukraineslovakia.sk/.
The Ukrainian government info line +380 934 185 684 is available for people from non-European countries(mainly students from Africa and Asia).
After crossing the border, every resident of Ukraine will receive temporary accommodation and meals. The assistance provided by the Slovak Republic to the citizens of Ukraine is free of charge. Ukrainian citizens will receive all important information from customs, volunteers or police officers.
Governmental and non-governmental organisations will also help and provide humanitarian and basic material assistance to every person who wants to refuge in Slovakia from the war.
Transport from the border crossing to temporary accommodation is coordinated on site. Some municipalities provide free commuter transport for the people of Ukraine. Taxi services are also available.
Some Slovak mobile operators provide SIM cards for calls and internet free of charge at the border.
From https://ua.gov.sk/en.html