There are three conjugation groups in Spanish verbs:

• First conjugation; verbs ending in -ar.
• Second conjugation; verbs ending in -er
• Third conjugation; verbs ending in -ir

All Spanish verbs belong to one of these three conjugations. Each group will have a specific set of endings for each tense. 
For example,
for -ar verbs, the set of endings for the present tense is:
for -er verbs, the set of endings for the present tense is:
for -ir verbs, the set of endings for the present tense is:
The set of ending will change per each tense, i.e: another set of endings for the preterite, another for the future, and so on.

All regular verbs will follow this rule, however in Spanish you will find quite a lot of irregular verbs, i.e: they do not follow the general rule, so they may have a different set of endings or they will have a different stem. Whithin the irregularities you will find different categories also specific for each tense.
That a verb is irregular in the present tense doesn't mean that it has to be irregular in all other tenses, but you will generally find verbs that are irregular in more than one tense. To give you an example, take the common verb hacer (to do/make). Let's see its irregularity in three different tenses.
In the three different tenses the stem has suffered a change, however the regular endings are the same as regular -er verbs.
Another common verb with irregularities is verb ir (to go). 
You can see again that both in the present and the preterite, there is a stem and ending change. However in the future tense bothe the stem and the ending are regular.