Planeswalkers are cast as spells, just like any other nonland cards. There's a number in the lower-right corner of each planeswalker card. That's its loyalty. It enters with that many loyalty counters on it, whether you cast the planeswalker as a spell or if it entered some other way. It needs those loyalty counters to stay by your side. If a planeswalker ever has no loyalty counters on it, it's put into the graveyard.

To proliferate, choose any number of players or permanents that have one or more counters on them. This can be any kind of counters: +1/+1 counters on creatures, loyalty counters on planeswalkers, even unusual things like time, charge, or doom counters.