The mixed conjugation consists of those verbs whose 1st person present and past forms are different (the past form will be one syllable longer) and whose infinitive form is more than one syllable.

It is probably the most complicated of the three conjugations as some of its verbs have palatalization changes depending on the tense. You can see this on the main Chart.

There are a lot of rules that govern how the verbs change, naturally, but once you recognize verbs and can tell what it’s doing from context and endings, it’s not too difficult to figure out.

You can read more about the different classes of verbs here.

Some books will refer to it was the 3rd conjugation, but this seems to be largely dependent on the author.

Below are the present (tagadne), simple past (pagātne) and future (nākotne) forms for sveicināt:
sveicināt — to greet
| tagadne | pagātne | nākotne
| vsk. | vsk. | vsk.
1. es | sveicinu | sveicināju | sveicināšu
2. tu | sveicini | sveicināji | sveicināsi
3. viņš/viņa | sveicina | sveicināja | sveicinās

| dsk. | dsk. | dsk.
1. mēs | sveicinām | sveicinājām | sveicināsim
2. jūs | sveicināt | sveicinājāt | sveicināsiet/sveicināsit
3. viņi/viņas| sveicina | sveicināja | sveicinās
Now let’s look at mācēt, which has a few changes in the present:

a palatalization change in the present tense,
drops the -a ending in the 3rd person present, and
shortens the 1st and 2nd person present endings from ām/āt to am/at.

mācēt — to manage
| tagadne | pagātne | nākotne
| vsk. | vsk. | vsk.
1. es | māku | mācēju | mācēšu
2. tu | māki | mācēji | mācēsi
3. viņš/viņa | mak | mācēja | mācēs

| dsk. | dsk. | dsk.
1. mēs | mākam | mācējām | mācēsim
2. jūs | makat | mācējāt | mācēsiet/mācēsit
3. viņi/viņas| mak | mācēja | mācēs
The reflexive form has its own rules about adding endings.


Replace the 1st person singular ending of -u with -os.
Add the reflexive endings to the normal verbal endings for the 2nd and 3rd person forms.
Insert a -j- when necessary to indicate that the vowels should not be paired.

Simple Past/Pagātne and Future/Nākotne:

Replace the 1st and 2nd person singular and 3rd person regular endings with reflexive endings.
Add the reflexive ending to the normal ending for 1st and 2nd person plural.

See how this works in the following example:
mācīties — to learn
| tagadne | pagātne | nākotne
| vsk. | vsk. | vsk.
1. es | mācos | mācījos | mācīšos
2. tu | mācies | mācījies | mācīsies
3. viņš/viņa | mācās | mācījās | mācīsies

| dsk. | dsk. | dsk.
1. mēs | mācamies | mācījāmies | mācīsimies
2. jūs | mācaties | mācījāties | mācīsieties/mācīsities
3. viņi/viņas| mācās | mācījās | mācīsies
There are more tenses, of course. I will add them later on, but these are the most essential to know.