No profit was made previous year (2010), but a bunch of expenses were done. No taxes were filed for that year. Typical start-up scenario.

Gains were made in year in 2011, so taxes would need to be filed for that year, but I wonder if expenses from previous year can be subtracted to compute net gain for the year 2011? If yes, what's the exact procedure?

I'm assuming net gains = income earned - business expenses for a self-employed individual. Correct me if I'm wrong.

Income averaging was repealed in 1986, sorry.
You have to deduct expenses in the year in which they were incurred.
You are just now doing taxes for 2011?
Yes, you subtract expenses from income. You need a 1040, Sch C, and Sch SE.
C lists expenses. SE is straight self employment tax for Social Security.
You should have started paying Estimated Quarterly's in 2012. Only the first year (which I guess since you didn't file for 2010 will be 2011) does not have to file each quarter.

What joypulv says is true for the most part. If you had other income in 2010, the losses from your business can offset that income.

If there was no other income, the losses can, in most cases can be brought forward to offset current 2011 income under a process called "net operating loss".

You must first file the 2010 and 2011 returns to document the losses with the IRS, then submit the NOL to bring forward the losses to 2011.

If you need professional help, email me at the email address on my profile if you cannot see it below.

Atlanta is right you need to amend 2010 and compute your NOL.

It is important to note that any NOL carryforward will not reduce your self-employment tax in 2011. I suggest you get professional advice to review your 2010 situation to see if any of your expenses can be capitalized so they can be carried forward and deducted against business income and save on the S/E tax as opposed to being expensed in 2010 with no offset to the self-employment income in 2011.

Good point, MLSNC, about the SE tax.