Your quote is slightly misleading as the rules are far more complicated than that and hugely depend on the TLD concerned, the registrar, and other factors. There is no hard rule on 30 days or anything. Let us say in gTLD it can be from 0+30+5 days (deletion at expiration + typical restore grace period + typical pendingDelete grace period) to 45+30+5 (same but with the full 45 days of autoRenew grace period). See this official diagram:
In any cases, expired or not, you buy domains at registrars. So you will first have to select one or more that are accredited in that given TLD (again, depends on the TLD).
At its current registrar (typically: see whois results on the name), you may be able to find the name being auctioned. You can either bid and try to get it, or you wait for it to be dropped (deleted), at which time either some people did program a "backorder" which is an automated way to register automatically domains that suddenly become available again (and you will have no chance to be faster than those, so if really interested by that domain you may want to shop around and see if any registrar can backorder it for you, do note however that some will make you pay even if they fail securing it for you), or noone is interested by it, it goes back to the pool of all available domains and you buy it like any other free domain.
In short it mostly boils down to select a trustworthy registrar with enough features you need and ask it to help you secure that domain.