US company can profitably make and sell widgets for $98 each. Chinese company sells them for $80. President imposes a 25% tax on widget imports, raising the Chinese price after import tax to $100. US company sales surge.

Other US company that uses widgets in their manufacture of other product for export wail and gnash teeth that now their exports are uncompetitive. (Or US company that issues widgets to staff to enable providing services have to cut back, have layoffs, etc).

There may also be some anomalies depending on how it's implemented. These tariffs can sometimes be a bit ham-handed. For example, I can see a situation where tiny solar cells not meant to be targeted are swept up in the tariffs.

The tariffs would be imposed by the Department of Commerce which takes policy direction directly from the President.

(the department also gives advice, but the authority and responsibility ultimately rest with the President)

He appoints the regulatory reps that are alligned with his policies. Add personal dynamics and diplomacy and you have a rather big role.