There’s no general answer on this.

Hostels might be booked out during summer. 
Some hostels have dynamic pricing, other hostels have always the same prices, other hostels have higher prices on weekends, others have higher prices during summer months (July, August)…

Also depends on the countries you are traveling in and the exact destinations.

Thanks for the quick response.

Thinking of Berlin, Warsaw, Prague, Budapest, Vienna and Ljubljana. 

How early on do places tend to get booked out in the summer?

Well, you are going to some of the hotspots, so there are a lot of options available in most of the cities.
Budapest for sure will not be fully booked - there are so many hostels.
Ljubljana doesn’t have that many hostels, so it might be fully booked
About Warsaw don’t know.
Prague has a lot of hostels but the good places might be fully booked.
Berlin has a lot of hostels, but the cool places might be fully booked. Same for Vienna.

So in general except Ljubljana you should also find last minute mostly something (but still difficult to predict after last two summers with corona how extremely it will increase this year - some places are already again on the level of 2019 or even above!).

Disclaimer: All without any guarantee. Just from my experience.

Depends on the Hostels you wish to book. Mixed dorms or private 1 person bedrooms?
As for the latter, it might help but that answer has been given by @MartinM.
As for the first, dorms are mostly the cheapest option anyway and I don’t find many difference in the price for booking beforehand or the day before.

When I was in Ljubl-in the mid of pandemic last yr-I noted plenty=dozens of hoStels-on quite nice spots too-but well over half of these were closed.

Its daft simple to check a few sites like hostelworld or booking (also does most hoStels) for what/where etc. Do not expect any lower prices the longer you wait-if lucky it stays the same

And just think: due to covid many had to close-distancing is not really very well possible in most, and current situation is on flux. Also do be aware that in East-EUR many are not used so much for globettrotting juniors, but often for foreign laborers (the POlish work in GB and IE-so in PL now work plenty of Ukraynians and Latvians)

@JAW looking for mixed dorms.

Thanks for the response!

@mcadv we were thinking of potentially going to Poland so this is interesting to know, thanks.