The best way to directly exchange links is by visiting sites similar to yours in size, scope, and topic; and then contact them asking about link sharing. It will probably be easier to get smaller sites to link to you than larger ones for right now since you are new, and I would recommend starting small and going for bigger sites as your own grows anyway. Similar new sites will usually be very happy to participate in some mutual backscratching, whereas bigger sites are very likely to blow you off unless you have some previous relationship with them in some way.
If you come across poorly by asking to swap links with an overly powerful site when you have a zero pagerank, it may hurt your chances of linking with them after you have grown if they remember it and retain a bad impression of you and your site. I would not advise using your only chance to make your first impression on any site that really matters until you are sure it is going to be a good impression. They may check your site out once, and then upon revisiting it later may not take the time to see that it has grown or improved; and may just think "Oh yeah, I remember this site" and not bother checking it out again.
Keep in mind when asking for link sharing that you don't have to have an awesome pagerank to get started, but having a zero is definately not a good thing when bargaining. Having a zero rating can mean that you have been penalized by Google in some way for bad practices, and many sites may not want to work with you. If you could just manage to get your page rank up to a one, you would have a much better chance of swapping links with another site.
You should definately look around on forums, etc to see if any people with similar content are looking for someone to share links with. When you post about it, be sure to indicate what kind of site you are wanting to build links on. For example: I myself have a new blog that I am actively working on building links for; but from reading your post I have no idea if your site might be a good fit to trade links with or not. Posting what type of site you are wanting to swap links for will vastly increase your chances of sucess.
A wonderful way to accumulate a lot of good backlinks right away is to register for as many directory sites for your blog or website as possible. Directories usually have pretty good page ranks, and their purpose is to link to other sites; which makes these backlinks really quick and easy to get. There are tons of directories, and a good number of them are free to use.
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I would also recommend using all of the other major social bookmarking sites to bookmark all of your posts or articles. Just make sure that you bookmark plenty of other good quality content that you enjoy or find useful and not just your own, or it makes you look very bad.
Once you have used the directories and social bookmarking sites to give yourself an initial boost, you should hopefully no longer have a zero pagerank. You will not have become an internet giant, but it will at least allow you to come to the link-sharing table with some bargaining chips