As a group leader, according to the circumstances I have three kind of positions.
First, there are rare moments where I can hire on my core budget: that is basically when my group was created or when the person hired moves to his next step. These are positions where it is extremely hard to fire, so I would rank social skills very high.
Second type, I sometimes get a grant for a project with enough funding to hire one person. In that case it is essential to hire somebody who is technically compatible with the project and who is able to deliver under time pressure. (Unfortunately, more and more post-doc positions are like this. I strongly dislike this system, and I am very tempted to downsize my research to rely more on consumable grants and collaborations and less on that kind of top-down research, but it is very had to do as research institutions become increasingly addicted to overheads, and will always prefer PIs with big grants.)
Third, there are cases of post-docs who obtain their own funding. As mentioned in another comment, it can take a lot of time to secure the funding. Often, the project sent to the funding agency will be ironed out together. This phase is actually a good test to see if the applicant and the lab are a good match; and if it is not the case, the project will not be exciting and the risk of accidentally ending up working together will be very low...
Some of this may sound a bit negative, but my message is: think about science: where are the labs that do something that you want to learn, which are the research environments in which you think you will expand your mind and keep it young, and reach out these places early, by meeting their researchers at conferences, by collaborations, by giving seminars, by contacting the lab heads directly, etc. If you only rely on open calls you will miss many opportunities and you will waste a lot of time, as many of them are there for only... ahem... administrative reasons. Aim at the best, and if you do not find, consider another job and do not look back :)