You have two options when deciding which fields you want to see in OpenCRM: Customising the Field Access or Layouts.
The second will also allow you to move fields around the screen. You can read more about using Layouts here.
This FAQ deals with the first option: Customising Field Access.
This option allows you to choose which fields are visible to your users without having to set or change their location on the screen. You can do this system wide or by profile.
To hide a field from all users of your system, you will need to go to Settings and select "Default Organisation Field Access". From here you will select which module you would like to edit.
Simply untick those fields you do not wish to see and click Update.
If instead you wish to hide fields only for certain users, you will need to first make sure these users all share the same profile (or the same set of profiles). You can find out more about setting up and using profiles here.
Go to Settings and select "Field Accessibility and Customise Search." You will then need to choose which module you wish to edit.
You will now be able to select the Profiles for those users you do not want to see these certain fields.
Then on the next screen, simple untick the fields you don't want them to see and click Update.
You have the option to make certain fields visible but not editable. You can also customise the Basic and Advanced Search options from this screen (find out more about this here).