Melissa-
That's a little ambitious given your skill level, but doable. That table looks like it does not have any fancy joints, but you may have a hard time finding plans. I suggest that you look at basic furniture-building books at your local library to see how those corner joints are made and go from there.

There are various ways to make joints like this; the most typical ones involve: 1) doweling, which requires a special jig and a drill press, or 2) mortise and tenon joints, which require a table saw, a drill press and a mortising jig (or skills with a chisel that take years to get good at), or 3) biscuit joinery, which requires a special power tool. If you try to build a table this massive and only hold it together with screw/nails and glue, it will loosen up and come apart over time.

Other tools needed would include a number of bar clamps to hold everything together during glue-up.

I would find this a fairly easy project, but I have a complete woodworking shop, and have been working with wood for 50 years. I'm not trying to discourage you, but I just want you to appreciate that this is a little ambitious for someone who is just starting. However, we only learn by trying, so, if you are feeling up to a challenge, you should try it. Good luck.

Appreciate the honesty. Yeah, i know its ambitious but when you don't have the money to purchase a new vanity, you have to think outside the box a little. I want to show you a picture of what my vanity area looks like and you tell me if there is another way I can work this out.

I was hoping that by using the wall studs to attach and support the vanity I might be able to do a simpler version of the vanity? Or perhaps a floating type vanity where attaching the legs is not an issue?

Thanks so much for your help!

Found something that I'm hoping will work. Wondering if I could use this plan and modify to make a 23"x 60" vanity. The only concern I have is whether the table will hold up the weight of vanity. I plan on tiling the countertop and using a vessel sink. Here is the basic idea on how to build whats called a parsons table and the link with more details http://www.popularmechanics.com/home_journal/workshop/2846191.html?page=1:

missy-
I took a look at the complete plan at the web site you posted. Overall, I think it's do-able for you, but I'm going to make some observations and suggestions for your consideration.

1. That design will support the weight of a vanity. However, it would be much better if, once it's built, you screw through the back top edge and into the studs. The main problem in scaling up is that you are making the legs a lot taller and, though they can easily support downward pressure, the joint connecting the legs to the top is not a particularly strong one: any movement of the vanity could exert a lot of leverage on the joints, and weaken them or loosen the legs considerably. The advantage of the first design you posted is that the lower shelf added considerably to stability by locking things together.

2. The picture of the Parsons table is beautiful, but the reality, particularly as you are a beginner, is that the seams are going to show and may even be slightly out-of-flush where the legs meet the top. If I were building that table, I'd consider using solid wood for the legs, and use a table saw to remove the wood at the top to create the same leg design, but one with no seams running down the sides. Then, where the top, visible edge of the leg meets the bottom edge of the counter, I'd remove a small amount of wood from the leg so that there would be a visible groove (say, 1/16" X 1/16") where the two pieces meet. I always think it's better to do something like this because it hides a mismatch and looks like an intentional design element.

3. I also am not satisfied with the fact that they attach the leg to the top with only nails and glue, because that is a weak joint and hard to assemble so that the leg is really securely attached. It will be hard to install the legs and: 1) have them parallel, because hammering on them will displace them, 2) have the top of the legs tight into each corner after banging on them with a hammer. If you want the best joint with this design, you should put glue on the legs and then clamp them tightly into the corners with a couple of wood clamps. Then, you could drill through the faces where the nails would have gone and put in counter-sunk screws, instead. There is a special screw called a "Trimhead" that has a head not much bigger than a nail, and will not loosen up like the nails possibly will. Gluing and clamping like this will increase the chances that your legs will be parallel and square to the top.

3. Finally, what are you doing for a top surface? Are you planning on wood or tiling over it, or having stone or something?

By the way, if you have more detailed questions, please feel free to contact me directly by email using the link on my Member Page here. Good luck.

Kudzu9's advice is very good. For an inexperienced woodworker, the results that plan would lead to would bear only a loose resemblance to the photo. That smooth, unbroken matte black surface would be difficult to achieve and extremely short-lived. The table in their photograph is wearing more imperfection-concealing makeup than Cameron Diaz.

With some design changes like those that Kudzu9 suggested, and with somewhat moderated expectations, I'm sure you can build something you'll feel good about. Plans like the ones you linked to tick me off because they set people up for disappointment. The 'simple DIY project' is not what they photographed. The thing they photographed was not simple to produce.

I think you can buy really well-made square (hollow) 5x5's at the big orange lumber store as "porch posts", which would be a huge advantage to you, as they are square, true, and all ready to go. Buying enough suitable lumber and gluing up such stock is expensive and out of your tool's capabilities. The square 5x5's would probably be a special order, but still a good value. You don't want to use solid stock for these, as they will check.
You can make joints with a kreg jig system that will be suitable. The screws will be hidden on the backside. I think a good finish would be black milk paint coated with black wax. Very satin-y and elegant, though perhaps not as waterproof as a factory-applied catalyzed finish. But it will be serviceable 'cuz you can always touch up with more black wax.
Good luck.
Casey

sombreuil-
It is possible to have solid legs of those dimensions that won't check, as I've built things like this many times. But I should have pointed out that you need to make sure you are using quality, kiln-dried lumber, and to check carefully that the solid stock doesn't have warps or bows in it.

Obviously, it's possible to do solid glue-ups in any size given the right machinery and access to the required grade of lumber. In the OP's situation, such is not the case. I can see the OP struggling to make do with off-the-shelf HD grade #2 pine, and my heart goes out to him/her.
Casey