I understand Buddhists don't technically worship, but pray to the Buddha or meditate (apologies for any mistakes). My question is: do Buddhists have a certain number of times a day to worship/pray/meditate? And is there a certain day/days out of the week they congregate together to worship/pray/meditate?
There are Uposatha days, wherein one makes increased effort at following precepts (either being more conscientious of the five precepts or temporarily adopting the eight).
I gather that there is often more deliberate meditation or study as well on these days, in addition to precept following:
It is usual for lay people to go to the local monastery and to spend all day and night there. In different monasteries, of course, the way they spend their time will not be the same and much depends on which aspect of the Dhamma is stressed there: study or practice. Where there is more study, they will hear as many as three or four discourses on Dhamma delivered by senior bhikkhus and they will have books to read and perhaps classes on Abhidhamma to attend. But they are quite free to plan their own time with meditation, discussion of Dhamma with the bhikkhus and so on. In a meditation monastery lay people will get less instruction and that will be about the Practice of Dhamma, while most of their time will be spent mindfully employed — walking and seated meditation with some time given to helping the bhikkhus with their daily duties. So the whole of this day and night (and enthusiastic lay people restrict their sleep) is given over to Dhamma.
Then there are other various holidays and festivals. I'm not sure if any of the other holidays involve increased practice or not. Some seem like they would just involve paying respect to the Buddha (Vesak) or monks (Kathina Ceremony).
First of all, in your question, "but pray to the Buddha" is not technically correct, as we cannot "pray" (assuming the meaning of the "pray" as praying to external being ie, god) to Buddha (He is no longer here to listen to the prays). We pay respect to Buddha (, Dhamma and Sanga). However in a way I agree with you that some people actually "pray" to Buddha. I don't think it will result in any benefit, though.
OK, about the questions, according to my understanding and experience:
Do Buddhists have a certain number of times a day to worship/pray/meditate?
The answer is NO.
Is there a certain day/days out of the weak they congregate together to worship/pray/meditate?
The answer is Quite NO.
However, during the full moon day (in countries like Sri Lanka), we observer "Uposatha sil". In some cultures, this happens every week accordance with the four phases of the moon.
Anyway, in practice, when it comes to daily routine, we like to start the day by paying respect to Buddha, Dharma and Sanga and end the day by doing meditation at least for 5-10 minutes.
Further, when it comes to actual meditation, I think you can do it with most of your daily activities. You could do "breath meditation" when you are waiting to the bus, or do some walking meditation, when you are walking to your work etc.
Speaking from my experience with Western Buddhist communities: There is usually a day (or more) in the week where members of the sangha can meet and meditate together. But that is not a specific day, just when it is convenient for the organisers.
The tradition goes that the Buddha attained enlightenment or nirvana when he was a youngish man (around thirty). He elected to continue as part of the world spreading the Dharma for another 50 years only achieving final release on his death - his parinirvana. I find this very evocative.
Anyway for us it's an opportunity to re-engage and deepen our practice. To really get stuck in - with the other members of the community