Below are some points to help you prepare for the loss of a degu:

Realise that all life must come to an end.
Spend some time with your degu and let them know you care.
Plan in your head what you will do when the time comes and where you would like your degu to be buried- this will make it much easier for you later.
Know that you have given your degus the best life possible, and that they get as much out of being with you as you do from them.
Be prepared to ask a vet to put them to sleep- this may be kinder to your degu if they are suffering or in pain.

When the time comes:

Cry- it is much better to let it out than to hold your feelings in.
Talk to someone close- they will understand and help you to grieve.
Talk to other degu owners, they are more likely to know exactly what you are going through.
Have a look at the farewell sets on www.rainbowbridgepets.co.uk for a coffin and grave marker for your degu.
Prepare the burial site and don't be ashamed to say a few words of remembrance.
Vent your anger or frustration by shouting or talking out loud.
Go for a walk- this can help to clear your head.
Remember the good times with your degu, don't dwell on the bad.

Afterwards:

If you need to, visit the place your degu was buried.
Send Degutopia a picture of your degu in happier times for the memorial page.
Make sure any remaining degu(s) are coping with the absence and not showing signs of depression.
Move the cage 'furniture' around to distract any remaining degu(s).
Clean the cage thoroughly, including toys (replace if necessary)- this will help remove the scent of the departed degu and is reported to improve the mood of any remaining degu(s).
Spend more time with any remaining degu(s). If only one degu remains, it may help to consider the advice on the introducing degus guide.