Draw your weapon with a straight line, using a ruler. Most anime weapons are sturdy and unmoving until swung or manipulated (swords, staffs, spears), so they should be drawn as such. Consider the material your weapon is made of (metal or wood), which will help you create the design details.
Add the mechanism to your weapon at the topmost point of your initial line. For a spear, this will be an arrowhead or metal bayonet. For a scythe or machete, this will be a rounded knife point with a razor-sharp edge.
Embellish a sword handle with short, horizontal lines wrapping around the hilt. You can even insert Japanese characters or samurai symbols into the handle to give it ultimate authenticity.
Create depth by adding a glint of light on the knife blade of your metal weapon. Using a burst pattern (asterisk), you can easily create a glint of light on the tip of a sword or even on a shield.
Add weaponry effects to give your fantasy anime character motion and charisma by adding sweeping curves, stars or wind around the movement of each weapon. Especially for graphic art (comic book) anime, weaponry effects denote magical powers or super strength--two things that are ideal for anime heroes.