I don't know a lot about how preparing spells works. I know that some classes have to prepare their spells and others don't. I couldn't find any information about Warlocks.
You're right that the PHB could be clearer about this in certain places, for example in the Spellcasting Chapter under the heading "Known and Prepared Spells" (PHB 201), we find:
Members of a few classes, including bards and sorcerers, have a limited list of spells they know that are always fixed in mind.
No specific mention of Warlocks there, though they're included in the "few classes". If you compare the spell table for Bards (PHB 53), Sorcerers (PHB 100) and Warlocks (PHB 106), you will see they have a similar column 'Spells Known' and this leads to the answer to your question.
As with Cantrips for other spellcasters, the Warlock's 'Spells Known' column says how many spells they know, without needing to prepare them. In in-game logic terms they are gifts from the extraplanar being with which the Warlock has the pact.
This is spelt out in the rules for Warlocks (PHB 107):
The Spells Known column of the Warlock table shows when you learn more warlock spells of your choice of 1st level and higher.
Again I can see the confusion, as 'learn' does not necessarily mean 'always have available', though that is what it means for the Warlock.
The way Warlock spells work can also be confusing if you are coming from the Basic Rules, where Spell Preparation seems 'standard', but in fact Spell Preparation is a feature added to Clerics and Wizards, but not to Warlocks.