I am assuming you are in the USA.
In the USA, there is a big difference between hiring contractors and employees. If you don't know the difference, please ask another question here (or search the internet). Briefly, contractors are basically using their own equipment and working on their own schedule, whereas with employees, you are telling them exactly what to do. There are a lot of details and the IRS gets very mad when you misclassify an employee as a contractor, so make sure you understand which you are hiring.
For hiring employees, whether full time or part time, you are responsible for a whole bunch of complicated payroll deductions, tax withholding, insurance, workman's compensation, and more. For most companies, it is worth hiring a payroll service like PayChex or QuickBooks Payroll (integrated with QuickBooks accounting software) to make sure that you do it right. There are a lot of tax forms to file before you hire employees. Every state's tax department publishes a guide on how to start a business, and the IRS publishes one, too. These guides list all the things you need to do. It took me about a week to set everything up right to hire my first employee. The easiest thing is sometimes just to hire an accountant.
For hiring contractors, whether directly or via an online service, it's much simpler. You simply pay them 100% and then file a tax form called 1099-MISC at the end of the year. They are responsible for their own taxes.
Since contractors are simpler to pay than employees, a lot of small businesses try to pretend their employees are contractors. The IRS does not like this one bit.
You also asked if outsourced work can be considered an "expense" when filing taxes. Absolutely. Everything you spend on your business is an expense that gets deducted from your business's income when filing taxes, as long as it's an "ordinary and necessary" business expense. Again, the details are extremely complicated, so it's a good idea to spend a few days reading up on it, or hire an accountant to help you.