Hi blessmerized games! Welcome to the forums and 2009! In answer to your question, it all depends on whether you want to work in 2d or 3d.
2d animations
For 2d, you can use "Paste Image" or sprites - the two are very similar, so we'll just use sprites as these are probably easier. Firstly, use a bitmap editor to create a series of images that make up the walking cycle. It's a bit like a Disney film, every frame in a scene is of the same character, but each frame is just that little bit different.
Each frame must be loaded into DarkBasic using either "Load Image" if each frame is a separate file, or "Load Bitmap" and "Get image" if all the frames are stored in a single bitmap image. IMPORTANT - all images when loaded in DB should be the same width and height!
Now we're ready to start the animation. Say the animation images run from 1 to 25. In the main loop, we call this command:
Sprite Sprite, X, Y, Image
Sprite is the animation number, X and Y are the screen coordinates of the top left corner, and image is the number of the image used when the sprite is drawn to screen. This examplecode shows what goes on, though don't take it as an example to compile!
rem Load images into slots 1 to 25
Add your load image code here :-)
Frame = 1
Sync On
Do
Sprite 1, 50, 50, Frame
Inc Frame
If Frame = 26 then Frame = 1
Sync
Loop
An image will appear on screen at (50, 50) and each image of your animation will be played ("Inc Frame" makes the sprite move to the next animation frame every time the program loops around). When the animation comes to an end at frame 25, the variable Frame will increase to 26, so we just reset to 1 to make the animation loop again.
Now, suppose we have an animation of a character walking from left to right across the screen. At the moment, he'll just be walking on the spot. So, we increase the X-coordinate of the sprite every loop. How much we increase the x-value depends on how far the sprite appears to move in the animation frames:
rem Load images into slots 1 to 25
Add your load image code here :-)
Frame = 1
X = 50
Sync On
Do
Sprite 1, X, 50, Frame
Inc X, 2
Inc Frame
If Frame = 26 then Frame = 1
Sync
Loop
With this, the sprite will move 2 pixels across the screen each time the program loops. You can change the y values as well, to allow full movement over the entire screen.
3d animations
DB uses a limb-based animation system for 3d objects. In a 3d model of a human, fpor example, the upper arm is a mesh, the lower arm is a mesh, and the hand is a mesh, but all three are linked together in a certain order called the limb hierarchy. As the upper arm mesh is moved, the lower arm and hand meshes automatically change position. Also, only the keyframes (the most important frames) need to be set as DB is clever enough to fill in the gaps and create smooth animation.
To use one of the sample objects (you probably have DarkMatter 1, so lets pick the knight figure for the sake of argument), you simply load it using "Load Object". To play the animation it contains, call "Play Object" to play the animation once only, or "Loop Object" to make the animation play forever.
Now, if you use the walking knight model, he (like the sprite) will walk on the spot. To make him move, you need to use the "Move Object" command. This will move the object the specified distance in the direction it is facing. So, bringing that together:
Sync On
Load Object "Knight walking.x", 1
Loop Object 1
Do
Move Object 1, 5
Point Camera Object Position X(1), Object Position Y(1), Object Position Z(1)
Sync
Loop
Two things to note - "Point Camera" is merely a hasty and not very good way of keeping the camera following the 3d object so you can see it move away. Without other objects as a reference point, you might not notice any movement at all.
The other thing to note is that again, the move distance may not be quite right for the animation. The animation and the actual movement produced are independant, and so you really have to play about with this until you find a value that makes it look good.
If you want to create your own 3d animations, you can do it manually with the rotate/position/scale limb commands. You can do it slightly moreeasily with a proper 3d animation program, like my
Lightning Limbs 
. My site hasn't been updated in a while, but expect a newer version sometime in the next 2-3 months.
Hope this hasn't been too much of a bore!
"I wish I was a spaceman, the fastest guy alive. I'd fly you round the universe, in Fireball XL5..."