Best for her to go to the immigration office or, or should I go there or is there another way ?

You get work permits at the labor office, not immigration.

She should go there and ask if it's possible, and if it is, what she'll need to do.

As said, work permits are issued by the Ministry of Labour, not immigration. More information can be found at MoL website here.

You do not advise the basis of your current permission to stay. If married to Thai, and your permission to stay is based on extension of stay through marriage, you can use that to support your work permit application. Or if you currently hold Non-Immigrant O or B visa you can use that to support WP application too, otherwise you will need to obtain Non-B visa from consulate abroad. Details of the papers required can be found in this link.

Remember that working in Thailand without a work permit is illegal and if caught can lead to jail time, but is often reduced to a fine and deportation.

As said, work permits are issued by the Ministry of Labour, not immigration. More information can be found at MoL website here.

You do not advise the basis of your current permission to stay. If married to Thai, and your permission to stay is based on extension of stay through marriage, you can use that to support your work permit application. Or if you currently hold Non-Immigrant O or B visa you can use that to support WP application too, otherwise you will need to obtain Non-B visa from consulate abroad. Details of the papers required can be found in this link.

Remember that working in Thailand without a work permit is illegal and if caught can lead to jail time, but is often reduced to a fine and deportation.

Also keep in mind that there is a list of jobs which are prohibited for non Thais, the list is on this site under the appropriate thread near the top of the forum.