Ben Finney,

There are two ways.

1) Database Level.

2) Code

1) Database Level:

Instruciton: Make sure that user has the access control of that model which you can to access from that menu.

Key points:

If user doesn't have the access control for particular model than user will not able able to see those menu which trigger the information of that model.

Here you go!

How to create access control for groups?

Setting>>Technical>>Security>>Access Control List

Create access control for model/object for specifc group if doesn't created.

How to assign Groups to Menu?

Setting>>Technical>>User Interface>>Menu Items

Search your menu and add groups of that Users group.

If you want to uniquely identify this user than create your own group or else use the existing group which is assigned to that user.

Creating your own group.

Setting>>Users>>Groups

By following this steps you can achieve your menu access from database level.

2) Code.

i ) You need group to use in access control, either use existing group or create your own.

ii) Create access control list for that user group with particular object/model.

iii) If there are already access control created and menu doesn't appear than assign your group to that menu.

Here you will find document how to create groups and access controls.

Click Here 

Hope this will help.

Rgds,

Anil.