Death

[beatle1957]

How do you bury your family member on your lot ?

[Grim Reaper]

In The Sims 3 Pets for PS3 you can't.  After the Grim Reaper comes you see a grave or urn depending on where you sim turns to a ghost (urn for inside grave for outside).  Then, after the Grim Reaper does his speech and your sim is officially a controllable ghost the urn or grave disappears.  The only option after that is to live our the time period for a ghost, given the chance to bring them back to life through a few methods or send them directly to the netherworld.  I've seen a message for The Sims 3 Pets for PS3 that you can put your pet's grave in a cemetery for piece of mind but you can't.  I've gone to Gilman Hill Graveyard and Goth Cemetery and have tried going through the inventory where the pet's grave appears and nothing.

Sorry I cannot help.  I haven't played The Sims 3 directly.

[Kronos]

On the base game for the 360, as far as I know you can't bury a sim. All I got was an urn when the sim died. I moved the urn outside and it turned into a gravestone. I haven't had one of my created Sims or family Sims die yet. Just the npc that died at my birthday party.

[karlissa]

I've done this before and I'll do it again

You can get tombstones of dead sims there are 2 ways to do it, 1 is for sims you have in your household, 2 is for ones you don't
Method 1
Step 1: Let the sim die as normal
Step 2: Catch them with a ghost zapper (inventing) or with a cat (hunting)
Method 2
Step 1: When the sim has just turned into a ghost (or for old age when grim talks with a speech bubble with them in it) use the capture interaction so the tombstone doesn't disappear, since when a sim dies on console they are temporarily invisible and have an interaction to destroy the tombstone and delete the sim but you interrupt it with this method and the tombstone stays .

[Grim Reaper]

I've done this before and I'll do it again

That's really cool.  I may try that.  Thanks for sharing.   I've always wanted tombstones of different shapes and sizes just for decoration, not necessarily that had actual sims.  It would make for a creepy mansions backyard or something.