Here's a simple example that meets your requirements halfway. You can adapt it as necessary.
This example uses uicontrol to add a push button and questdlg for the callback on the push button. The dialog box has to be closed before the user can interact with the plot again.
If you're interested in learning more about dialog boxes, check out the Dialog Boxes and Notifications section. You could use modal message boxes instead of a question dialog box too. Have a look at the linked example.
See this link to learn more about uicontrol properties and customization. You might be interested in the CData property of a uicontrol object to set an icon.
numFaces = 600;
[x,y,z] = sphere(numFaces);
figure;
ax = pcshow([x(:),y(:),z(:)]);
title('Sphere with Default Color Map');
xlabel('X');
ylabel('Y');
zlabel('Z');
f=ax.Parent;
c = uicontrol(f);
c.Style='pushbutton';
c.String = 'Info';
% c.Units='Normalized';
c.Position = [10 400 50 15];
c.Callback = @displayInfo;
function displayInfo(src,event)
answer = questdlg('Put all the information over here!', ...
'Info', ...
'Ok','Ok');
end
