To get elected in any office you need the support of your political party and backers with deep pockets. The more people you know in your party, the better off you will be for the former but it is also who you know that's important. It is also more important to have a few influential backers than many less influential ones.
My fellow editors are right. Money is clearly the first order of business for any politician, of course. People who are willing to work at the grass roots level are another essential element. Experience is important, of course, but this political season has shown us that it may not necessarily take political experience to be successful. One other element I would add is connections. A networking system is a must for today's politicians. Personal qualities and convictions aside, these are the most important things a politician must have in today's world.
It is very rare to see someone who has no political experience getting elected to office. Voters believe that is important and this is the way in which you win party support. Those who do run for office without political experience are usually in no-win races anyway.
Pohnpei's exactly right in that you need money to win a statewide of national race, but starting with the 2010 elections, you need a ton of it. The 2008 Presidential election was our first billion dollar race, but now because of the Citizens United Supreme Court ruling, outside groups can also spend as much as they want to advertise for you. This means in addition to needing money, you'll need the support of big business and action groups with a lot of cash to back you up, or your opponent will just outspend you.
Footsoldiers help with everything from sign posting to phone banking to doorbelling, but it only matters on election day, so a concentrated Get Out The Vote (GOTV) organization can make the largest difference, getting as many of your supporters to the polls as possible to vote. A candidate can't do that by themselves or with ads, it has to be done by the volunteers that support them.
This really depends a great deal on what level you are talking about. However, I would say that money is extremely important at most levels.
I would say that the higher the level of political office you are running for, the more important money is. You need money to buy television ads, to pay for people to call potential voters, to conduct polls to find out what the voters think and on and on.
At the lower levels of politics, a very important resource is "foot soldiers." At those levels, it is important to have lots of people who are willing to talk to their friends, go door to door, and do other sorts of "retail" politics to get your message out.
In all cases, it helps to have "resources" like a good personality and speaking ability, of course.