Can anyone suggest ways in marketing my website

Depends if you're talking free or paid advertising. If you can buy go to: overture, or google ad words. If free then build your affiliates.

I think another good suggestion is to find some like-minded forums, put together a nice signature, and start posting on those forums a lot. If your posts are genuinely helpful, curious people will click the links in your sig.

I haven't looked at your site, but if it's what I suspect (articles for free or purchase), then you should track down some Web sites for writers, and start posting on their forums.

Note that you DON'T post about your site. Don't spam. You just post generally helpful things, and your signature speaks for itself.

-Tony

Provide something original that the hundreds of other article sites don't provide. This is really your only chance in my eyes, article directories are all over the place and most are all the same.

I have a site, and the traffic there is not that bad but I check the statistics and see that users leave after seeing a couple of pages. Do you think a chat or something like that would help and does it keep people really? I do not know much about chats, how would I choose a good one?

Register in high traffic, quality forums and add your site's link in your forum signature and make meaningful posts. Add new articles and update your site regularly with informative content. If people find something helpful they will return and also recommend it to others.

I agree join quality forum share some thought with your link as a signature. Submit to directories. Put more quality contents on your site.

yeah, well... This is a problem of many site, and mine was kind of a dead place for some time when I launched. A plain chat though is not that cool, though at first I had flashcoms.com chat installed and it's very nice, but then I came up with idea to make a schedule of topics to discuss and then users come for that specific thing. That really increased traffic, so you can try this

Adding your link to your email and forum sigs,
Writting a press release
Writing articles about your sites topic
Word of Mouth
There are lots of ways....

Here's some ideas swiped from some articles I've written:

Start a paper newsletter. Although there are printing costs and postage costs involved with a hard copy newsletter, it will spread the word about your website to people who are not otherwise online on a regular basis. At T&S Web Design, we are in the process of starting a simple, one page newsletter that will be mailed out monthly to clients and potential clients.

Start an email newsletter. Have a place on your website where people can sign up for the latest updates on your business. Just make sure that you include unsubscribe information as well.

Write articles in your field of expertise, and include a link to your website.

Exchange links with related websites. Make sure that they are not directly competing with you but have the same target audience that you do. You can exchange text links or banner ads.

Submit your link to directories. If you have a vacation home in New Mexico, search the web for "vacation home New Mexico." Look through the first two pages of results and contact all the website owners that have sites listing multiple vacation homes in New Mexico. Give them the info about your vacation home and about your site, and see if they'll list it. Chances are, many of them will he happy to list it for free, because the more that they have listed, the more people will visit their site, too.

You should always carry a business card with you. Just like in your ad, there's much more room on your website for information than there is on your business card. And if you have pictures of yourself on the website, people who have forgotten exactly who you were will have their memory jogged.

In your emails, develop a little mini-signature. I have the following on the bottom of my emails:

Tim
Senior Web Designer
T&S Web Design
http://www.tandswebdesign.com
http://www.getasiteonline.com
XXX-XXX-XXXX

I use a similar, but shortened, version of that signature on forums I frequent. Anyone who has any online correspondence with me should have no trouble finding my website.

You can also find unusual ways to promote your website that are specific to your business. An arcade I do the website for prints their website address on their redemption tickets. Another includes it in their monthly publication. Yet another has an upcoming infomercial. The sky's the limit!