Hi, Sherri. This is a common problem and usually easily fixed but there are degrees of damage and how much you will have to do to remove the spots. Start by putting a layer of petroleum jelly on the spot and leaving it over night. The oil in the jelly has a greater affinity for the finish and drives the oil out.
If this does not work, take a soft cotton cloth and fold it into a tight ball. Lightly dampen the cloth with denatured alcohol and rub it lightly and briskly over the spot. Do not rub hard or leave the cloth on the table. If you have ever seen anybody French polish furniture, you want to use the same kind of light, rapid strokes and you want the cloth to be in the same slightly damp condition.
There are further steps that you can take, Sherri, but if you try the 2 steps listed above, one of them will probably work. Post back if they don't and we can go on to the next step.