We are exporting products manufactured in Europe to USA and recently
we are under the gun because our prices are in $ and our costs are in
Euro, therefore we see profits declining every day. I understand that
there are some possibilities of "hedging" currency in order to limit the
risk and the exposure, but I am totally unfamiliar with them (I am not a financial
guy). Can someone explain me what could be done to improve the
situation in plain English and with practical examples and - maybe -
some ballpark figure for associated cost ?

Put crudely - you have missed the boat

The idea of hedging (exchange rates) is to 'lock' your exchange rate
so that currency fluctuations do not matter to you.

In your case your income is in USD so you sell forward USD for Euros.
Effectively you are now just trading in Euros.

Instead of selling forward you could buy an Option to sell USD
forward, that insulates you from the USD going down, but if it goes up
against the Euro you just don't take up the Option.

Personally I reckon that the USD is grossly undervalued against the
Euro and GBP, and that although it may go down a bit, it is more
likely to rise over the next year.

In general when you have large import bills or export orders it is
prudent to buy/sell forward so you simply do not care what happens to
the exchange rate.

The big danger is that one could get involved in complicated Treasury
deals that initially look as if they are making more money than the
rest of the company, and then pull the company down. Hence, keep
things simple.

One cautionary tale, a friend of mine recently told me how his company
got stuffed. They had substantial export orders to be paid for in USD.
They sold the USD forward to cover their position. The dollar went
down, no problem, but the bank that they had done the deal with went
bust.