You should talk to an accountant or tax preparer for your jurisdiction, who can give you all of the relevant rules and information that you need.
Essentially, though, there are two ways to “write off” equipment.
The first, and most common, is “depreciation” of capital equipment used in the execution of your business. For example, you have a computer that you use – for business purposes! – let’s say for invoicing, your own accounting, even tax preparation, customer records, purchasing, all sorts of “business activities” (generally, you have to be prepared to show that the machine is used “for business only”, or claim only a part of it as business and the rest as personal – non-depreciable). But let’s say that you have a computer that you use 100% for business. Your rules may allow for “accelerated depreciation” of this equipment, because it’s recognized that computers “age” (from a utilitarian viewpoint) rather quickly. So perhaps you take 50% of the computer’s value as depreciation on your business tax return in the first year of ownership (or 50% of the value of the used machine, if that’s how you acquired it) in the first year after you purchased it or put it to use in your business. The next year’s depreciation might be an additional 30%, and the final year, say 20%. What that means is that after three years of ownership and use in your business you have written off the full value of the computer. That is, you have noted a negative hit on your earnings from the business as the value of the computer has decreased over time. (The flip side of this is that if you do sell the computer in the fourth year or any year after it is fully depreciated, you have to note the total sale price as income.)
The second way of writing off assets is via capital / catastrophic loss. That is, equipment and goods that are lost in fire or flood or through theft, vandalism, embezzlement, etc. I have no advice for you on this; it’s something that varies so much (from jurisdiction to jurisdiction, and sometimes even from year to year as tax codes change) that you really need to talk to a professional about how to document the loss (since you’ll have to prove your investment AND your loss). You might even be able to claim losses as a result of changing market conditions, but I’m much less certain of that.
For example, if you own a large inventory of iPhone 3s when the iPhone 4 is introduced, then your stock of brand-new equipment just got a lot less valuable if you had bought it not knowing about the introduction of the iPhone 4. So the items still have some value, and you can still sell them, but maybe for not even as much as you paid. In that case you will take a regular loss on the sale, which will, of course, be “written off” against profits you made in the business, assuming there were any. (And if there weren’t, and you ended up taking a loss for the year, then you could probably take the “carryover loss” to offset profits a year or two later – depending on the rules where you pay taxes.)
Of course all of this presupposes that you ARE filing a tax return that includes “business income”, and that the business has a profit motive AND does, in fact, turn a profit (I think in the US the general rule is “at least one year in three” must be profitable, otherwise it’s a hobby and none of this stuff is “depreciation”, it’s just hobby expense and has no bearing on taxes at all.
You need to know the rules for your tax jurisdiction and your business to make informed choices and file the correct tax returns.