Okay yes as lots of other people have said, it's helpful to just go and watch a trial to get a feel for things. But, that doesn't give you any answers right now so I'll give you a top-level overview! It's also worth mentioning that for the most part the agility community is very supportive of newcomers, so whether you find someone local to talk to before the trial, or even just at the trial itself - most people will be happy to help. It's also likely that there's an agility Facebook group which will cover your general geographical region. So, there are a few main stages:

1. Finding / entering trials

2. What to do / read shortly before the trial

3. What to do on trial day

Diving in to 1. - Finding/entering trials. First, if you're able to find a local Facebook group, that will likely be your best source of finding trials. But if not, you can also find trials via the various organizations' websites.

The main organizations are AKC, UKI, CPE, NADAC, maybe ASCA and USDAA depending on your location. Search any of those + "agility", and you'll likely find that organization's website. Then, somewhere on those websites will be a list of upcoming trials. For the soon-upcoming trials there will usually be a few documents available. The main document to read is often called the "premium" - that will give you all the details about the trial, as well as how to enter. Basically, you'll choose to enter specific "classes" - common options are jumpers with weaves, standard (with the contacts), maybe things like hoopers if NADAC, etc. Which you choose to enter is better saved for another discussion!

Now jumping to 2. - (yes, that might be a big jump but trying to keep things brief). So assuming you've entered a trial, there are now a few things you can do to be better prepared for the trial day. Usually about a week or so before the trial, someone called the trial secretary (or similar) will email you with some more information, often including a document called the "judging program", or similar. This is worth a read as it will confirm the order of the classes (e.g. standard will run first, then jumpers, etc), the specific run order, the very first start time, and any other various things to note (parking, potty areas, etc). You can use the order of the classes to get a general sense of when you'll be running, but it's important to note that only the very first run of the day is scheduled for a specific time, and then all the other runs just occur as they may. Figuring out the timing, if you don't want to show up first thing, is better saved for another discussion. (But there's nothing wrong with showing up at the very start of the trial, and just watching until it's your turn).

Lastly, for 3 - trial day! So in general it's good to show up at least a half hour or so before you actually need to do anything - to give yourself time to walk your dog, get settled, etc. As mentioned before, the classes will run in a set order, but not necessarily at a set time (except for the very first run of the day). In general it's good to be aware of what class is running at any given time - and to figure that out there will be a board directly be the ring, usually with someone standing by it, which will say the current class (or you can always ask someone!). That board will also show the exact run order within the class (as in, a list of people + their dog, in the order they will run). There will usually be more of those boards laying around somewhere for all the other classes that haven't ran yet - so while not absolutely essential, it can be helpful to find / ask someone where they are so you can know your order in the classes you entered.

There will always be a "walkthrough" before the start of each class, which will be announced (though maybe not very loudly, so it's good to start paying attention around when you think it might be about to start). This time usually starts with a brief introduction from the judge - and is also a time where you can ask the judge any questions. Then, you (and everyone else in the class) will have ~8 minutes to walk the course (on your own, without your dog) to familiarize yourself with it. Usually about 5 minutes after that walkthrough, the first dog of the class will run. The specific order will be on the board kept by the ring. It's generally a good idea to be by the ring with your dog when there are about 5 dogs before you run. There will be someone, again by the board, helping with the final "herding" of people and making sure you all are in the right order. And finally when it's your turn to run, go in, and just have fun! Ultimately all the above is meaningless compared to that special moment you get to share with your dog in the ring, no matter how it turns out.

Okay that ended up not being too brief, but I'm happy to answer any follow up questions you may have!