The short conjugation consists of those verbs whose infinitive form is one syllable long and whose 1st person present and past forms are two syllables long. As always, prefixes and suffixes are not counted when figuring out conjugations.
Aizmest, mest and mesties are all considered 1st conjugation verbs because aiz- is a prefix and -ies is the reflexive suffix, neither of which are considered for conjugation purposes.
According to one of my references, this conjugation is considered closed, which means that new verbs aren’t being created in this group. Still, as fluid as languages can be, I would take this with a grain of salt.

Below are the present (tagadne), simple past (pagātne) and future (nākotne) forms for nākt:

Note the change from k to c for the past form and the 2nd person present singular.
nākt — to come
| tagadne | pagātne | nākotne
| vsk. | vsk. | vsk.
1. es | nāku | nācu | nākšu
2. tu | nāc | nāci | nāksi
3. viņš/viņa | nāk | nāca | nāks

| dsk. | dsk. | dsk.
1. mēs | nākam | nācām | nāksim
2. jūs | nākat | nācāt | nāksiet/nāksit
3. viņi/viņas| nāk | nāca | nāks
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 stems for the 2nd and 3rd person forms.
Remember to make any palatalization changes.

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.
When necessary, lengthen the vowel in the stem for the past tense.

See how this works in the following example:
celties — to rise
| tagadne | pagātne | nākotne
| vsk. | vsk. | vsk.
1. es | ceļos | cēlos | celšos
2. tu | ceļies | cēlies | celsies
3. viņš/viņa | ceļās | cēlās | celsies

| dsk. | dsk. | dsk.
1. mēs | ceļamies | cēlāmies | celsimies
2. jūs | ceļaties | cēlāties | celsieties/celsities
3. viņi/viņas| ceļās | cēlās | celsies