It depends. While you can go and make a round of the top job boards due to the sheer volume of jobs they have, you should also look at Job aggregators like Indeed and Simplyhired. Linkedin is another good source. Use the following method on Linkedin.
Search for graphic designers, artists, etc. in your target location and list the companies with their websites. If they have a careers page, apply or email or use the contact form. You can also try hr@domainname.com if nothing is available on the website.
If you're looking for jobs in the game industry (which covers many of the positions you listed), then you're not going to find open positions on a site like Monster.com or something like that. Searching for those kinds of jobs requires you to apply directly through a company's website most of the time.
You can check out the links I've provided below to find out the best way of finding and applying for those jobs. The first link is an article about finding jobs in the game industry, and the second is a link that provides the locations of many game companies around the world.
For jobs in animation, you're best bet is to employ a similar strategy, like applying directly to Pixar, ILM, Dreamworks, etc, or looking up advertising companies in your area and applying directly through their website.
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I am looking for either a graphic design, graphic artist, animation, or game design position.
