In probably all Indo-Germanic languages - at least in Spanish, French, Italian, Persian, English, German and Latin - the change of verbs follows a certain logic. It's hard enough to learn this logic and then there are exceptioins to this logic, which makes things not even easier.

Of the irregular verbs, there are two types. The first are the ones that change only their way of writing (not the way they are spoken). They are only in their spelling different to ensure the regularity of the spoken language. In the spoken language, they are not even irregulars. Let's have a look at an example.

vencer = to win
same logic:
convencer = to convince

with convencer: yo convenzo, tú convences... yo convencí, tú convenciste... yo convenza, tú convenzas... etc.

As you can see, vencer changes its stem in the first person singular in presente indicativo and in all the forms of the subjuntivo. This is only a different spelling to ensure the phonetical consistence. If not changed the the first person singular in presente indicativo would be:

venco = spoken: venko

Now it would be irregular because the sound of [c] would change to [k]. This is due to the rule that before the vocals a and o c is spoken k. These kinds of irregularities are derived irregularities.

Then there are the genuine irregular verbs that change not only in spelling but also in the way they are spoken. We will give an overview that include the imperfect, which actually has hardly any irregularities but it's easier to learn this way.

There are about 2,000 verbs, 1,000 of those have some kind of irregularity. But don't worry there aren't 1,000 different irregularities but only about 80. Most of them follow a certain scheme. Some verbs have more than one irregularity. One of those is colgar = to hang.

colgar = to hang

This verb shows two changes. The o turns an u, and after g is an u added (again because of the pronunciation rule that g is spoken with a throat-sound when it is before i or e). Therefore, it is tú cuelgues and not tú cuelges. In the following we have distinguished between genuine irregular verbs and derived irregular verbs. If a verb has two irregularities, a genuine one and a derived one, it is to be found among the genuine irregular verbs only.

We now will have a look first at the genuine irregular verbs and the first ones are so irregular that even the imperfect is irregular.

Within the group of verbs ending on -ir or -er this is the only one with this change. There are more in the group of verbs ending on -ar.

similar: contar = to tell (a story)

following the same scheme:
concordar = to agree, to put accordance
consolar = to console, to comfort
denostar = to insult
soldar= to weld
jugar= to play

with concordar: yo concuerdo, tú concuerdas..., yo concorde, tú concordaste...yo concuerde,
                        tú concuerdes...
with consolar: yo consuelo, tú consuelas..., yo consolé, tú consolaste...yo consuele, tú consueles... etc.
with denostar: yo denuesto, tú denuestas ..., yo denosté, tú denostaste... yo denoste, tú denostes... etc.
with soldar: yo sueldo, tú sueldas ..., yo soldé, tú soldaste... yo suelde, tú sueldes... etc.
with jugar: yo juego, tú juegas..., yo jugué, tú jugaste..., yo juegue, tú juegues... etc.

following the same scheme:
discernir = to separate, to distinguish (mentally, acoustically, visuallyl)

with discernir: yo discierno, tú disciernes..., yo discierní, tú discerniste... yo discernía, tú disciernías ... etc.

following the same scheme:
reír = to laugh
competir = to compete
conseguir = to get, to receive, to achieve
corregir = to correct etc.

with reír: yo río, tú ríes..., yo reí, tú reíste... yo ría, tú rías... etc.
with competir: yo compito, tú compites..., yo competí, tú competiste... yo compita, tú compitas... etc.
with corregir: yo corrijo, tú corrijes ..., yo correjí, tú correjiste... yo corrija, tú corrijas... etc.

Following the same scheme:
reconocer = to recognise
merecer = to deserve
parecer = to seem
convalecer = to convalesce
restablecer = to re-establish
endurecer = to turn hard

with reconocer: yo reconozco, tú reconoces...yo reconocí, tú reconociste...yo reconozca, tú reconozcas ...
with merecer: yo merezco, tú mereces... yo merecí, tú mereciste...yo merezca, tú merezcas...
with restablecer: yo restablezco, tú restableces...yo restablecí, tú restableciste...yo restablezca, tú restablezcas..
with parecer: yo parezco, tú pareces...yo parecí, tú pareciste...yo parezca, tú parezcas...

similar: reproducir = to reproduce

following the same scheme:
conducir = to drive, to conduct (a car)

with conducir: yo conduzco, tú conduces...yo conduje, tú condujiste...yo conduzca, tú conduzcas... etc.

following the same scheme:
erigir = to erect
exigir = to demand
fingir = to pretend
restringir = to contain, to dam
sumergir = to submerge
etc.

with erigir: yo erijo, tú eriges..., yo erigí, tú erigiste... yo eirija, tú erijas ... etc.
with exigir: yo exijo, tú exiges..., yo exigí, tú exigiste... yo exija, tú exigas ... etc.
with fingir: yo finjo, tú finges..., yo fingí, tú fingiste... yo finga, tú finjas ... etc.
with restringir: yo restrinjo, tú restringes..., yo restringi, tú restringiste... yo restrinja, tú restrinjas ... etc.
with sumergir: yo sumerjo, tú sumerges..., yo sumergiste, tú sumergiste... yo sumerja, tú sumerjas ... etc.

following the same scheme:
seguir = to continue (also change of e -> i)

with seguir: yo sigo, tú sigues, él sigue, nosotros seguimos..., yo seguí, tú seguiste... yo siga, tú sigas ... etc.