Working out tax owed

Hi

I have (hopefully) got the forms together for my husband to file his taxes.
He arrived here in April 2015, and was working in the US up until then, he now has a job over here which he started in June.

He has previously always used an accountant, so this has been a learning curve.

As far as I am aware it is
1040
2555
8965
Schedule E (as he rents out his house in the US)

My main question is, how does he work out what (if any) taxes are owed on the rental income? 

Thank you for any help you can give me.

There may be State taxes on the rental income. He is required to claim depreciation as a rental expense.  You'll have to decide if you want to use ACRS or MACRS & know the lower of cost or market value of the building.  Because of the depreciation he may have no current taxable profit.

If he has a UK bank account he'll want to file Schedule B and maybe an FBAR.  If he is in a UK pension plan he'll have to decide if he wants to elect into the Treaty.

You've made a good start and Guya has pointed out some possibilities. As your husband has US source income you should understand the difference between UK taxation on an arising or remittance basis and which country has primary taxation authority so you can claim the correct foreign tax credits.