How can I draw the following aldehydes and ketones: hexanal, heptan-3-one, 3-methyloctanal?

Let's go through each of these individually.

Hexanal:
First off, when naming compounds, recognize the longest chain of the molecule. As an example, for hexanal, notice that the word "hexa" signifies that the longest chain contains six carbon atoms. As a first step (Step 1), we can draw out the hexa- backbone. Next, we would look for any functional groups that we could add by looking either at the prefixes or the suffixes. In the case of hexanal, there are no prefixes, but only the suffix -al. This represents an aldehyde, which has the form #CH=O#. The next step would be to identify where in the hexa- backbone the aldehyde appears. This info is usually given to us in the form of numbers, as we will see later. In this case, however, since aldehyde can only occur at the end of a molecule (i.e. they are terminal functional groups), their numbering is always at the 1 position. This is shown below in Step 2:

Heptan-3-one:
Here, for Step 1, we identify a hepta- backbone which means that the longest chain contains seven carbon atoms. For Step 2, we identify the suffix -one as referring to a ketone, but this time, since the ketone functional group is not always terminal (i.e. at the end of a molecule), we must figure out where in the molecule the ketone occurs. This is where the numbering comes in -- the molecule name tells us that the ketone is at the 3 position. Again, there are no prefixes, so Step 2 has only one part. See the image below for the steps.

3-methyloctanal:
For Step 1, we identify an octa- backbone which means that the longest chain contains eight carbon atoms. For Step 2, we identify two functional groups - one prefix and one suffix. This means that there will be two sub-steps for Step 2. For Step 2a, let's look at the 3-methyl prefix. This means that we must place a methyl group at the three position. For Step 2b, we again see the -al suffix, which must be at the 1 position. Note that Step 2b can be performed before Step 2a, but that you will still get the same answer.