There is some info on this site - titled "island hopping" on the menu on the left hand side (and I´ve tried to add a link to another useful site in the URL section of this thread - hope it comes through for you).
You can easily catch a ferry to Playa Blanca, not only to Armas and Fred Olsen run, but there is a small boat - Lineas Romero - a cheaper option but as the boat is smaller, I wouldn´t suggest using this on choppy days
, especially if you get sea sick.
The fastest option is the Fred Olsen Catamaran - which takes around 25 mins - so not long at all.
Prices can vary but are usually more expensive if you buy them from the actual office in the port, whereas other vendors in the port, that also offer excursions can offer you a better deal - so take a look around and you should be able to save quite a bit on the list price. (Residents do receive a decent discount...something to be aware of...as I once heard an angry couple arguing with someone at a ticket office because they misread the prices - I don´t know how!
...and were upset when they realised they had to pay more than residents.)
Staying over in PB shouldn´t be a problem, but make sure you book in advance, don´t just turn up, as occupancy rates around the Canaries are very high at the moment.
Its up to you if you plan a day trip, or longer. If you want to see more than Playa Blanca, then stay over. Or why not fly into Fuerte, take the ferry to PB and then spend a bit of time in Lanz and fly out of Lanzarote airport too? Obviously you wont get to see all of both islands - but you´ll get a mix - just a thought if you like to move around a bit.
(Oh and if you plan to hire and car and take it with you on the ferry you need express permission from the car hire company and usually a stamped document too. The ferry company won´t let you on without it. I´ve done this with Cabrera Medina the other way round, from PB to Corralejo and back again.)
Hope this helps you Lizzy.