NOTE: Sorry for its ridiculous length; this guide covers everything about running a server on a Mac using Notch's Vanilla Server software

Note: This was only tested on Mac OSX 10.5.8, as I do not have Snow Leopard on my machine.  Please forgive me if I am not able to help you because of that.

Instructions for Notch's Vanilla Server

• Download Notch's Vanilla Server Here
• Go to Applications>Utilities>Java Preferences
• Move Java SE 6 to the top of both of the lists
• Open Terminal
• Type cd /Users/YOURNAME/Downloads/minecraft-server or, instead of typing the whole path, just type cd and drag the minecraft-server into terminal
• Then type java -cp minecraft-server.jar com.mojang.minecraft.server.MinecraftServer (you can write a .sh file to make this operation go much faster, that will come later in this guide)
• Now, if you followed all of the directions above correctly, it should start generating a number of files such as the server.properties, the server_level.dat, the admins.txt, players.txt, banned.txt, etc. etc.
• When that is all done, close it, and write the .sh file for it.
• Write cd (complete path to the minecraft-server folder) on the first line, and on the second line write java -cp minecraft-server.jar
  com.mojang.minecraft.server.MinecraftServer
• Then to make the .sh file executable, open terminal, type cd (path to minecraft-server folder) and press enter
• now type "chmod +x minecraft_server.sh" (minecraft_server.sh is only an example name, you can name it whatever you want)
• now quit terminal, and right click minecraft_server.sh and click "open with" and click "choose application"
• click where it says "recommended applications" and change it to "all applications," and click the checkbox that says "always open with"
• Now navigate your applications folder to get to Terminal (Applications>Utilities>Terminal) and press OK
• Now double click the minecraft_server.sh and it should open terminal and say that the server is running on port 25565 and a few other things as well
• For a visual guide on what it should look like and what it should say, here is a picture that Jonnyabc took

Instructions for Omen v0.70

• Download Omen v0.70 Here
• Unzip Omen070.zip and drag the Omen070.jar to the root directory of the minecraft-server folder
• Double-click Omen070.jar, and Omen should open up
• When you open Omen, it loads the server_level.dat that the server generated.  More information on this in the next section.

How to use Omen v0.70 (Credit to Snake on the Minecraft Forums)

NOTE: Snake did indeed use windows for his tutorial, but everything is the same when using Omen on a Mac.  In fact, Omen was developed on a Mac, so there is absolutely no reason why it shouldn't work on a Mac.

The Main Screen

Here, I will
be going over the parts of the main screen. View the image below and
read the descriptions from the corresponding numbers of the parts on the
list under the image.
I'll separate the main screen into two parts,
the Stage half and the Editor half, for sake of space.

-The Stage Half

1. File. This opens up the File tab. This contains the New map command, Open map command, etc.
2. Edit. This opens up the Edit
tab. This contains many commands, such as Undo, Quick Caves, etc.
3. View. This opens up the View tab. This contains commands such as Show
Grid, Zoom In, Zoom Out, and the like.
4. Tools.
This opens up the Tools tab. This contains commands such as Brush,
Replace All (2D), etc.
5. I call this the
"Stage Information" line. This shows what layer you are viewing, the
tool you have selected, the size of the brush, and the X, Y, and Z
coordinates of the place you last clicked on the Stage.
6. The Stage.
This is where you edit the map. Simple enough.
7. Layer Up. This
moves one layer up, but appears moves one layer down.
8. Layer Down.
This moves one layer down, but appears moves one layer up.
-This is
because it is moving up and down by numbers. 0 is the top of the map,
and one layer minus the depth of the map is the bottom. So if you moved a
layer up from the top of the map, or layer 0, you would move to layer
1, but move one layer lower than the top of the map. This is the same
for layering down except you're going up.
9. Zoom In. This simply
zooms the camera on the stage in. This is useful for precise editing of
the map.
10. Zoom Out. This zooms the camera on the stage out. This
is useful for large-scale editing of the map.
11. X-Z. This is the
default viewing of the map, or an overhead view.
12. X-Y. This is a
side view of the map. Useful for making the map in a box, like I will
show you how to do in another section of this tutorial.

-The Editor Half

13. Block Types. This is where you select the block you want to use.
-A. Air. Useful for "deleting" blocks on the map.
-B. Stone.
-C. Grass.
-D. Dirt.
-E. Cobblestone.
-F. Wood.
-G. Tree
Sapling.
-H. Bedrock. Also know as Op Block, Opcrete, Adminium,
Admincrete, Admin Blocks, etc.
-I. Water.
-J. Still Water.
This water does not move unless disrupted. To disrupt it, you usually
just place a block next to it, and then delete it.
-K. Lava.
-L. Still Lava. This lava does not move unless disrupted. You disrupt it the
same way you do water.
-M. Sand.
-N. Gravel.
-O. Gold Ore.
-P. Iron Ore.
-Q. Coal Ore.
-R. Tree Trunks or Logs.
-S. Leaves.
-T. Sponge.
-U. Glass.
-V. Red Cloth.
-W. Orange Cloth.
-X. Yellow Cloth.
-Y. Lime Green Cloth.
-Z. Green Cloth.
-AA. "Seaweed" Green Cloth. (As I call it.)
-BB. Neon Blue Cloth.
-CC. Blue Cloth.
-DD. Light Purple Cloth.
-EE. Purple Cloth.
-FF. Light Pink Cloth.
-GG. Pink Cloth.
-HH. Hot Pink Cloth.
-II. Dark Grey, or "Black" Cloth.
-JJ. Grey Cloth.
-KK. White Cloth.
-LL. Yellow Flower.
-MM. Red Flower.
-NN. Brown Mushroom.
-OO. Red
Mushroom.
-PP. Gold.
-QQ. Iron. Often called Silver, although it
isn't silver.
-RR. Double Halfblock. Also known as Double Stair
Block.
-SS. Half Block. Also known as Stair Block.
-TT. Brick.
-UU. Trinitrotoluene, or TNT.
-VV. Bookcase Block.
-WW. Mossy
Cobblestone.
-XX. Obsidian.
14. Brush. The basic tool of Omen. I will go over this tool in another
section of this tutorial.
15. Flood
Fill. Contains six flood fill tools.
16. Line.
Draws straight or curved lines between two points.
16(2). Sorry, I added a second 16 in by mistake. This is the brush size
slider. It goes from 0 to 512.
17. Prefabs. Allows you to place
premade objects, such as Trees and Ruins. I will go over this tool in
another section of this tutorial.
17(2). Sorry. These are quick buttons for basic brush sizes.
18. Selection.
Contains only one tool, the Dropper tool.
18(2). Sorry
again. 2D Brush. This makes your brush two dimensional and only places
blocks on the layer you have selected. This is set by default.
19(2). Round Brush. This simply makes the brush round.
20. 3D Brush. This
makes your brush three dimensional and places blocks on the layer you
have selected, but only if the brush size is over 4. Useful for making
spheres or cubes. I will go over doing that in another section of this tutorial.
21. Square Brush. Simply makes
the brush square. This is set by default.
22. Centre Brush. Centers
the brush I'm guessing? I've never needed to use it, but I always have
it selected. Doesn't seem to make a difference if I don't have it
selected, though.
23. Replace Brush. This allows you to replace
blocks of a different kind with the block you have selected. Even if you
go out of the parts of where the blocks you want to replace are, it
will only replace that type of block with the block you have selected,
and nothing else.
24. Brush Density. Set at 1.0 by default. If you
make it below 1.0, (for example, 0.5), it gives the brush an airbrush
effect.
25. Session information log. Tells you how long it took to
generate a map, if what you loaded was loaded successfully, etc.

NOTE: If you have any questions, post them on this thread, and they will be answered.