Once you have changed your role to 'Approver' top right of your screen, you will find two sections: the 'Expenses for Approval' and 'Unsubmitted expenses'. If there are trips to approve a third section at the bottom of the page will appear.
Choose a user in the first section and click on the name to see all his/her submitted expenses.
If there are no strange expenses in the overview, you do not have to open expense by expense. You can approve all the expenses at once, by activating the checkbox (above all the expenses). All expenses will be selected and in the 'Actions'-button that appears you can now choose 'Approve'. To customize your overview, get more info in Custom columns in expenses overviews.
Whenever you do want to take a closer look at an expense, you can easily find all the details by clicking on the expense. If your administrator has granted you permission to edit an expense, the 'Edit'-button will be visible for you in the detail of the expense.
When you reject an expense you will need to provide a reason. The user will see this reason and will be able to reply to it and resubmit the expense. The expense will then be sent back to you, the approver, with an extra alert telling you that this is a rejected expense. Or the user can delete the expense if it was indeed a mistake or against company policy.