There are some exceptions but the procedure is usually : get a job offer from an employer that is willing to sponsor you, then talk to a lawyer... But a lawyer might be able to help you find ways to immigrate without a job offer, but that seems pretty unlikely to me.
The H-1B visa would normally be one of the 'classic' ways to be authorized to work in the US in your situation, the problem being that in recent years demand has far exceeded the available number (annual cap). For example this year 199,000 petitions were received during the first week, for only 85,000 H-1B available (including 20k for holders of advanced US degree). Therefore the USCIS now holds a lottery to determine which petitions will be reviewed first, and once 85k petitions are approved, you have to wait another year to apply...
The cost for an H-1B is nil for an H-1B as the employer has to pay for it and cannot ask you to reimburse those fees. You might have to pay in order to have dependants (wife, kids) added to your petition though.
The problem used to be to find an employer willing to sponsor you for the visa (the difficulty varies greatly depending on your industry), now the H-1B visa cap makes it more of a time issue unfortunately.
Other options you might look into depending on your how long you would like to work in the US: J-1 for an internship, E-2 for a company whose 'nationality' is the same as yours, L visas for a transfer to the same company in the US, F-1 visa for studies, and the O-1 visa which I will let you research by yourself and/or discuss with an attorney (the qualifications aren't as difficult at they may seem, trust me)