In short: Lithuanian personal pronouns decline by case, while possessive pronouns (mano, tavo…) don't. Below is a reference: personal, possessive, reflexive and demonstrative pronouns in one place — with notes on what you actually need for A2 and which points can be tricky.

Personal pronouns

Singular

Case (question)IyouhesheExample
Nominative (kas? — who?)tujisjiAš einu (I go)
Genitive (ko? — whose?)manęstavęsjojosdėl manęs (for my sake)
Dative (kam? — to whom?)mantaujamjaiMan patinka (I like it)
Accusative (ką? — whom?)manetavemyli mane (loves me)
Instrumental (kuo? — with whom?)manimitavimijuojatikiu tavimi (I trust you)
Locative (kur? — where?)manyjetavyjejamejoje

Plural

Case (question)weyouthey (m.)they (f.)Example
Nominative (kas?)mesjūsjiejosmes mokomės (we study)
Genitive (ko?)mūsųjūsųbe jūsų (without you)
Dative (kam?)mumsjumsjiemsjoms
Accusative (ką?)musjusjuosjaspas mus (to us)
Instrumental (kuo?)mumisjumisjaisjomisties mumis (towards us)
Locative (kur?)mumysejumysejuosejose
Kur jie?
men or a mixed group
Kur jos?
women & feminine-gender things

jie or jos? "They" in Lithuanian depends on gender. About forks (šakutės) you'd ask "Kur jos?", but if there's a spoon among them (šaukštas, masculine) — then "Kur jie?". A single masculine item in the group is enough to make "they" jie.

Possessive pronouns

Possessive pronouns don't decline — one form for every case, gender and number.

myyourhisherouryour (pl.)theirone's own
manotavojojosmūsųjūsųsavo
jo (his), jos (her) and jų (their) are the same forms as the genitive of the personal pronouns (table above).

The reflexive pronoun "oneself"

The word savęs ("oneself") declines like tavęs but starts with s-. It has no nominative form.

CaseoneselfExample
Genitive (ko?)savęsdėl savęs (for one's own sake)
Dative (kam?)sau
Accusative (ką?)saveAš save myliu (I love myself)
Instrumental (kuo?)saviminepasitiki savimi (doesn't trust oneself)
Locative (kur?)savyje

Demonstratives: "this", "that", "that over there"

All three demonstratives side by side, so every form is in front of you: šis (this, near), tas (that, neutral), anas (that one, far). They decline almost like adjectives.

Masculine

Case (question)this (šis)that (tas)that, far (anas)Example
Singular
Nominative (kas?)šistasanasTas, aukštas (that tall one)
Genitive (ko?)šiotoano
Dative (kam?)šiamtamanam
Accusative (ką?)šįanąPakabink šį prietaisą (hang this device)
Instrumental (kuo?)šiuotuoanuo
Locative (kur?)šiametameaname
Plural
Nominative (kas?)šietieanie
Genitive (ko?)šiųanų
Dative (kam?)šiemstiemsaniems
Accusative (ką?)šiuostuosanuos
Instrumental (kuo?)šiaistaisanais
Locative (kur?)šiuosetuoseanuose

Feminine

Case (question)this (ši)that (ta)that, far (ana)Example
Singular
Nominative (kas?)šitaanaAr tau patinka ši paprika? (do you like this pepper?)
Genitive (ko?)šiostosanos
Dative (kam?)šiaitaianai
Accusative (ką?)šiąaną
Instrumental (kuo?)šiataana
Locative (kur?)šiojetojeanoje
Plural
Nominative (kas?)šiostosanos
Genitive (ko?)šiųanų
Dative (kam?)šiomstomsanoms
Accusative (ką?)šiastasanas
Instrumental (kuo?)šiomistomisanomis
Locative (kur?)šiosetoseanose