Being the new kid in a Guild Wars guild has some unique advantages due to the way the game works. First and foremost, a low level cap means you won't be struggling for what feels like forever to catch up to your level 60 guild mates. Map travel is a significant bonus as well, since finding help for a quest or mission is much easier. Rather than hopping a mount and traveling for 15 minutes, your guild mates can map to your location in a matter of seconds from anywhere in game. If you take your time and choose a guild that is a good fit for you, feeling like a part of the crowd can come a lot more quickly than in larger MMOs.
Figure out what you want.
Take some time to think about what you are looking for in a guild. There are solid, well-established guilds in existence for nearly any play style you could think of. You probably already know if you want a PvP or PvE focused guild, but think a bit more. Do you care about Luxon or Kurzick faction? What do you like doing in game -- are you just starting out or are you cruising toward Legendary Master of the North? Are you all about the title grind, or more casual? Do you roleplay or prefer to keep things OOC? What about personal lifestyle and preferences? There are guilds for every preference: guilds for married couples, guilds geared toward women only or men only, guilds with minimum age requirements, and so on. Do you prefer an active guild buzzing with activity and chatter, or one with a slower pace where you can take your time and relax? Think of what time of day you play the most often, and see what guilds line up best with your playtime so you don't find yourself logging in every day two hours after the rest of the guild has gone to bed. It can be overwhelming, but just take a bit of time to think about your play style, and think about why you want to find a guild. What are you hoping to get from this? That will help your search immensely.
Be patient, look around.
Leaping headfirst into the first guild that offers an invitation is often a mistake. You're not the only one who has been tempted to jump in like that, but it's an easy way to find yourself guild hopping, becoming frustrated as no guild seems like a good fit. Take your time. Just because a guild is standing in Lion's Arch AD1 spamming that the first ten people to join get to be officers does not mean it's the perfect fit for you. Browse around, check out the guild recruitment forums on fansites. Take a look at what guilds are recruiting currently. If a recruiting guild has a link to a site or forum, browsing it can be an extremely helpful insight into the guild. Look around to see how active the forums are, if the site is up to date, and what sort of topics and events are being discussed. Does it hold your interest or make you want to read more? This may be a guild you want to check out.
If no recruiting guilds pique your interest, don't be afraid to reach out. Post that you are looking for a guild. Tell a bit about yourself and what you are looking for in a guild. If you've got things that are important to you in a guild, say so. Once you've gotten a few responses, explore them as listed above.
Okay, I found one that looks good, now what?
If you haven't already, look over their rules and guidelines before you join. Yes, they are lucky to have you, but they are also inviting you into their home, so to speak, and it behooves you to be respectful of the rules they have in place, and the guild members in general. Spend some time chatting with the guild leader or officer who invites you as well, to get a feel for things.
As with searching for a guild, once you've found one, don't be afraid to reach out in both the guild and alliance. Speak up when you join, say hi, join in the chat. If you're heading in for a dungeon or vanquish, let everyone know and ask if anyone wants to join. Similarly, if a group is gathering and it sounds interesting, jump in. Keep an eye out for upcoming guild and alliance events as well. It's up to your new guild to help make you feel welcome, but it's definitely a two way street, and you'll settle in much more quickly if you meet them halfway.
Don't forget that a new guild isn't going to fit like a glove five minutes after you join. Give it some time and allow yourself a chance to get to know your fellow members. If it's not feeling like a good fit, have a quick chat with the guild leader or an officer. You don't need anything extensive, just mention that you don't feel like you're settling in well and why. They may have some insight on how to solve the problem.
If you take the time to do your homework, find a guild that's right for you, and make the effort to integrate into your new guild, you should have smooth sailing.