An enthymeme is a syllogism that is incompletely stated. It is either missing a premise or the conclusion. For example,
All humans are mortal, so Socrates is mortal
is missing the premise that Socrates is human;
Humans are mortal and Socrates is human, so ...
is missing the conclusion that Socrates is mortal.
Indicator words will usually mark what type of sentence is missing, premise or conclusion. Determining the content of the missing item requires understanding the rules for a valid syllogism.
The basic idea is to use the principle of charity, if it is possible, to interpret the enthymeme as valid. This means that after adding the missing sentence, it will have two major terms, two minor terms and two middle terms. So, first standardize the two sentences that you already have as having four terms, two of which are the same. The missing sentence will be stated with the two terms that are not the same. In the first case above, 'mortal' appears twice and 'humans' and 'Socrates' occur once each. The new sentence will, therefore, be about 'humans' and 'Socrates'.
In the same way, if the two stated sentences are universal, the missing one will also be universal; and if the two are positive, the missing one will also be positive. If one of the stated sentences is particular (and the other is universal), the missing one will also be particular.
All of the above are required to follow the principle of charity; to interpret the enthymeme as valid.