Declining like adjectives
Active adjectival participles describe an ongoing action (like szczekający for "barking" or śpiący for "sleeping"). Because they function as adjectives, they must decline to match the noun they modify in gender, number, and case.
You do not need to learn any new declension tables for this. You simply apply the standard Polish adjective endings you already know.
For example, when modifying a feminine noun in the Genitive case, the participle takes the standard -ej ending:
Plural cases
When describing multiple animals or objects (non-masculine-personal nouns) in the Nominative or Accusative case, the participle takes the -e ending (forming -ące).
If the plural noun is in the Genitive case—such as after the preposition dla (for)—the participle takes the regular plural adjective ending -ych (forming -ących).
Masculine and Neuter cases
For masculine animate nouns (like dogs, cats, and birds) in the Accusative or Genitive case, the participle takes the -ego ending.
Neuter nouns in the Nominative case take the -e ending (forming -ące). However, if a masculine or neuter noun is in the Dative case (the indirect object, receiving something), the participle will take the -emu ending.
Bringing it all together
Whenever you use a participle, always check the grammatical role of the noun it describes. Notice below how krwawiący takes the -ą ending to match a feminine Accusative object (krwawiącą ranę), while śpiący remains in its basic dictionary form for a masculine Nominative subject: