What taxes do I have to deduct from my employees' check weekly?

If you want to be following all the tax rules correctly, you need to get some other resources besides just asking on here what needs to be deducted. That isn't just some simple question someone can easily answer in a post.

For one thing, where are you? I don't even know what country you're in, and wouldn't have any idea how taxes are deducted in another country. Plus there's likely local taxes no matter where you are. So that right there makes it difficult to answer.

I could only answer this from the point of view of the U.S. You would need first of all to make sure you have a tax ID number if you don't already have one. (If the only one you have is your S.S. then that won't work when you have employees.) You would need to get the Circular E from the IRS. That has all the information in it. You can call the numbers in the back if you don't understand how something works. The other tax is unemployment but all the info is in the same place.

Then there would be state -- most states have income tax, but some do not. You would need to call the state treasury office and find out, and then get the information from them about what needs to be done. There also might be a state unemployment tax, and some type of insurance (workers comp).

And there could be city. Even in my immediate vicinity, there's tons of different municipalities that all do their taxes differently, so even I have to call these places sometimes to find out their rates and get the paperwork that I need.

There's more complication to it than we can answer simply here. A better idea is to call the taxing authority in question and ask them, get whatever paperwork is necessary, find out what you need to be doing, etc. Then you can come on here and ask questions about specific things that you don't understand how to do.

You forgot the most important ones:
Federal Income Tax
Social Security
Medicare
The rest you have covered correctly.

Federal income tax, social security & medicare are all in the Circular E, which I did state would have the needed information in it. So yes I did cover it.

Sorry, I did not catch that.

You had it covered then.