A lot of skaters start by drawing out pictures of their dream park, and that's a great idea to get yourself excited, but first you need to Get Everyone On Board. First, you want to get a good group of skaters who will actually use the park, and who can be the face of the park building project. Skaters who are willing to help you put in the time and effort that this will need.
But skaters aren't enough. You need some other people from the community, too. Some people from your city government would be perfect - like your Parks and Rec department. Look for people who are looked up to in the community, who support your idea of getting a skatepark in your town. Maybe your pastor, or business owners? If you are a teenager, then perhaps some of the parents of the other skaters in your group. The more people you have on board, the better.
Once you have some people supporting you, you want to Approach the City to see what they think. This can be tricky, but it's where pulling in some of those respectable members of the community will help. There are good reasons to support skateboarding, and having a centralized skatepark cuts down on vandalism and other damage that skateboarding causes. The city may require something like a certain number of petition signatures, or they might have some other road blocks. The trick here is to work WITH the city, and help them to see the value of your dream.
Now, if the city just says no, then you can still go the private route - that means finding someone who will donate the space for a skatepark, and do it on private property. That's a lot more difficult, but it also means less city meddling. For this, you'll need to find a company or wealthy person who believes in the park like you do! Promoting and having an open meeting on the subject can help with this, if you need to.
No matter where you are building the park, you are likely going to need to Do Some Fundraising! The city SHOULD support the building of the park, but even if they do, you're going to probably need to come up with some of the money. Gather all of those supporters together, and have a meeting to come up with ideas! This can be a small meeting, or you can post flyers and have it in a huge public place - it all depends on your situation.
There are a MILLION ways to fundraise! Your Parks department may even have some ideas. There are small events, asking for donations, even going to local businesses and asking them to sponsor the park. Depending on your town, some people might be against supporting skaters - here is where you remind them that having a skatepark will centralize all the skaters, and keep you guys from terrorizing or damaging the rest of the town (even if that's not true). A skatepark is especially important in a town where skaters and the police have run-ins.
And donations don't just have to be money. You can get building materials from local suppliers and shops. You can talk to local charities and see if there's any way you can work with them.
You can also have some kind of big event, like a skateboarding competition to raise money for the new skatepark. Or a concert benefit? There are many ways to raise money...
During this time, or after, you can start to actually Design the Skatepark. This is probably the first thing you did, and it's a lot of fun. Keep in mind however that the park might very well look NOTHING like what you imagine. This can get frustrating, and you might be tempted to really pitch a fit about it, but don't. Unless you are some kind of prince, or independently wealthy land owner, you're going to NEED other people to help pull this off. This will be a group project. And that means letting go of your control. Besides, do you know what really goes into building a park? Maybe you do. But probably not. So, leave as much as you can to the professionals!
And there are MANY well made professional parks out there, made by people who would LOVE to come build a park in your town! Make sure you use one of these guys. Don't try to build one on your own - there's a LOT involved in building a concrete park that you and I wouldn't even think to be concerned about. USE A PROFESSIONAL!
The last tip, and the most important, is Don't Give Up. This process can take a looooong time. And, it can be discouraging. Some people will be firmly against it. Some people who support it will flake out. You might get bored, or distracted, or angry and be tempted to chuck the whole thing. Stay with it! Get the park built! You can do it!
For more help, here are some other online resources: