The bid is the price at which the market will buy a currency pair (before any commissions or fees), the offer (or ask) is the price at which the market will sell the currency pair (before any commissions or fees).
Most market participants have no difficulty determining the "bid" from the "ask" when they are dealing in their domestic or home currency. However, it can be complicated when dealing with a currency pair that differs from your standard FX requirements, or if you trade in a currency that is not your home unit.
FX rates are always quoted in terms of the unit currency, where 1 of the "unit" currency yields a set amount of the terms or settlement currency (the second currency in the pair).
For example, a USDCAD exchange rate of 0.9950 means that 1 USD will return .9950 CAD. Since the rate on the bid is always lower than the rate on the offer, it is then easy to determine whether you are on the bid or offer when asking for a quote.
AUD, GBP, NZD and EUR are all quoted in European terms against the USD. This means the foreign currency is always the ‘unit currency’ or the first currency in the pair (i.e. AUDUSD, GBPUSD, etc.). There are a few other minors and exotics that are quoted as such but in general, most other currencies are quoted in American terms with the USD being the unit currency.
This is important because once you understand the pair and direction (which currency you are buying, and which are you selling), determining which side of the market you should be quoted on is a breeze.
For example, with AUDUSD, one would buy AUD from the customer on the bid, thereby selling them USD. Alternatively, one would sell (or offer) the unit currency, AUD, on the offer and buy the second currency (USD).
An Australian company needs to purchase 100,000 US dollars to pay for imported goods.
The USDAUD quoted rate is 1.0625 on the bid and 1.0675 on the offer. By convention the USD is the unit currency and AUD is the terms currency.
The company will have to buy the USD on the dealer's offer, and will pay 1.0675 for each dollar bought.