As a tenant your responsibilities towards the landlord and the property will be laid out in your tenancy agreement. Most of your responsibilities will fall into two main categories, paying your rents and bills, and looking after the property and its contents.
As a tenant you are responsible for:
Paying the rent on time
Rent is typically paid one month in advance and must be paid directly (usually by direct debit) to your landlord or letting agent. Your tenancy agreement will stipulate whether rent is paid on a weekly, fortnightly or monthly basis.
Paying household bills (electricity, gas, council tax, etc)
While you are living in the property you are responsible for paying all household bills. If there are any overdue bills from the last tenant waiting for you when you arrive pass them immediately on to the landlord, you are not expected to pay for these.
Repairing damage caused by you or those living with you
If you damage the property or its contents, then it is your responsibility to rectify the damage or replace the item. Any damage that remains at the end of the tenancy agreement will be paid for out of your security deposit. Find out more about tenancy deposits.
If you redecorate the property without seeking permission from the landlord this may be viewed as damage to the property and you may be charged for putting it back to how it was before.
Keeping the house secure (setting alarm, locking doors, etc)
Keeping the property locked up every time you leave not only protects your possessions, but also prevents the property being damaged. If the property is damaged because you left the house unsecured, this could affect your tenancy deposit and possibly your insurance.
Keeping the house clean and tidy
Keeping the house clean and tidy will help ensure that the property and its furnishings are not damaged. If the house is unclean or untidy at the end of your tenancy agreement you may be required to pay for a professional clean out of your deposit money.
A tidy house will also make inspections go much smoother and quicker.
Returning the property in same state as you found it at beginning of the tenancy
When you are getting ready to move out of the property you need to make sure that the house is as clean as when you moved in and that any damages have been fixed.
If you fail to clean the house, the landlord can bill you to have professionals clean the house, the same applies if the landlord has to fix any damage to the property (and this can sometimes be more expensive than doing it yourself or sourcing someone to do the work).