The infra-red spectrum for a simple carboxylic acid

Ethanoic acid

Ethanoic acid has the structure:  

You will see that it contains the following bonds:
(1)carbon-oxygen double, C=O
(2)carbon-oxygen single, C-O
(3)oxygen-hydrogen, O-H
(4)carbon-hydrogen, C-H
(5)carbon-carbon single, C-C

The carbon-carbon bond has absorptions which occur over a wide range of wavenumbers in the fingerprint region - that makes it very difficult to pick out on an infra-red spectrum.
The carbon-oxygen single bond also has an absorbtion in the fingerprint region, varying between 1000 and 1300 cm^-1 depending on the molecule it is in. You have to be very wary about picking out a particular trough as being due to a C-O bond.
The other bonds in ethanoic acid have easily recognised absorptions outside the fingerprint region.
The C-H bond (where the hydrogen is attached to a carbon which is singly-bonded to everything else) absorbs somewhere in the range from 2853 - 2962 cm^-1. Because that bond is present in most organic compounds, that's not terribly useful! What it means is that you can ignore a trough just under 3000 cm-1, because that is probably just due to C-H bonds.
The carbon-oxygen double bond, C=O, is one of the really useful absorptions, found in the range 1680 - 1750 cm^-1. Its position varies slightly depending on what sort of compound it is in.
The other really useful bond is the O-H bond. This absorbs differently depending on its environment. It is easily recognised in an acid because it produces a very broad trough in the range 2500 - 3300 cm^-1.
The infra-red spectrum for ethanoic acid looks like this:

The possible absorption due to the C-O single bond is queried because it lies in the fingerprint region. You couldn't be sure that this trough wasn't caused by something else.

The infra-red spectrum for an alcohol

The O-H bond in an alcohol absorbs at a higher wavenumber than it does in an acid - somewhere between 3230 - 3550 cm^-1. In fact this absorption would be at a higher number still if the alcohol isn't hydrogen bonded - for example, in the gas state. All the infra-red spectra on this page are from liquids - so that possibility will never apply.
Notice the absorption due to the C-H bonds just under 3000 cm^-1, and also the troughs between 1000 and 1100 cm^-1 - one of which will be due to the C-O bond.

The infra-red spectrum for an ester

Ethyl ethanoate

This time the O-H absorption is missing completely. Don't confuse it with the C-H trough fractionally less than 3000 cm^-1. The presence of the C=O double bond is seen at about 1740 cm^-1.
The C-O single bond is the absorption at about 1240 cm-1. Whether or not you could pick that out would depend on the detail given by the table of data which you get in your exam, because C-O single bonds vary anywhere between 1000 and 1300 cm^-1 depending on what sort of compound they are in. Some tables of data fine it down, so that they will tell you that an absorption from 1230 - 1250 is the C-O bond in an ethanoate.

The infra-red spectrum for a ketone

Propanone

You will find that this is very similar to the infra-red spectrum for ethyl ethanoate, an ester. Again, there is no trough due to the O-H bond, and again there is a marked absorption at about 1700 cm^-1 due to the C=O.
Confusingly, there are also absorptions which look as if they might be due to C-O single bonds - which, of course, aren't present in propanone. This reinforces the care you have to take in trying to identify any absorptions in the fingerprint region.
Aldehydes will have similar infra-red spectra to ketones.

The infra-red spectrum for a hydroxy-acid

2-hydroxypropanoic acid (lactic acid)

This is interesting because it contains two different sorts of O-H bond - the one in the acid and the simple "alcohol" type in the chain attached to the -COOH group.
The O-H bond in the acid group absorbs between 2500 and 3300, the one in the chain between 3230 and 3550 cm^-1. Taken together, that gives this immense trough covering the whole range from 2500 to 3550 cm-1. Lost in that trough as well will be absorptions due to the C-H bonds.
Notice also the presence of the strong C=O absorption at about 1730 cm^-1.

The infra-red spectrum for a primary amine

1-aminobutane

Primary amines contain the -NH₂ group, and so have N-H bonds. These absorb somewhere between 3100 and 3500 cm^-1. That double trough (typical of primary amines) can be seen clearly on the spectrum to the left of the C-H absorptions.