-ащий/-ящий

1. Formation
This participle is formed from the 3rd person plural (они form) of imperfective second-conjugation verbs. Perfective verbs cannot form this participle because they lack a present tense.

• Take the они form: говорят (they speak) or светятся (they glow).
• Remove the final -т (or -тся for reflexive verbs): говоря- or светя-.
• Add -щ- and the appropriate adjective ending: говорящий. These participles decline exactly like soft-stem adjectives ending in a sibilant (the хороший declension pattern).
• For reflexive verbs, re-attach -ся at the very end: светящийся.

Note: First-conjugation verbs form this exact same participle using -ущий/-ющий. The same 'drop the -т' trick works perfectly for them too (e.g., читают → читаю- → читающий).

2. Meaning and Time Correlation
The present active participle describes an action happening simultaneously with the main verb, regardless of the main verb's tense. It translates to the English '-ing' form. Even if the main verb is in the past tense, the participle indicates an action that was happening at that same time.

3. The Sibilant Rule
Because you are building this participle from the они form, the Russian spelling rule (writing а instead of я after the sibilants ж, ч, ш, щ) is already taken care of for you. For example, дышат (they breathe) naturally becomes дышащий (breathing).

4. Reflexive Verbs
For reflexive verbs, the suffix -ся is always added at the very end. Unlike standard verbs, it never shortens to -сь, even after a vowel: светящаяся (glowing).

5. Stress
For verbs with fixed stress, the stress in the present active participle falls on the same syllable as in the они form (e.g., видят → видящий). For second-conjugation verbs with mobile stress (where the stress shifts to the stem in the они form), the stress in the participle usually falls on the suffix: курящий (from курят) and ходящий (from ходят). However, there are common exceptions among mobile-stress verbs that keep the stress on the stem, such as любящий (from любят), служащий (from служат), and дышащий (from дышат).

6. Usage and Register
This form is considered bookish (книжный стиль). You will see it in literature, news, and academic texts. In casual speech, Russians almost always use a clause with который. However, some participles have become standard adjectives, such as блестящий (brilliant).

7. Punctuation
If the participial phrase follows the noun it modifies, it must be set off by commas. If it precedes the noun, no commas are needed, unless it modifies a personal pronoun (like я or он), or if the preceding participial phrase has an adverbial meaning (usually expressing cause or concession), in which case it is set off by commas (e.g., Спешащий на поезд, пассажир забыл билет.).

8. Case Government
Participles retain the case government of the original verb for their own objects. For example, since the verb видеть takes the accusative case, its participle does too: видящий собаку (seeing a dog).