I received about 1/4 of my income from the first 8 month of last year from self employment. What expenses can I deduct for that time period? Business use of my home, internet, software, website hosting, website domain, etc...?
Without knowing the type of business you have or having your bank statements to see what you have spent money on regarding the business, there really isn't a way to give a complete answer. However, as far as home office expenses (utilities related to the home, rent or mortgage interest/real estate tax) there are 2 rules of being able to take those deductions.
In your example, no other activity (such as sleeping) can be done in that space during these 8 months you are trying to take the home office deduction.
Other common deductions are
I have attached a link that goes in much greater detail.