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Recetly I read that Sayanacharya's Bhashya on Vedas is Yajnika or ritualistic interpretation. So, I want to know what are the schools or means of interpretation of Vedas?

Yes, as we know that for better understanding of Vedas, the knowledge of Vedangas viz. Vyakarana, Nirukta, Chhanda etc. is essential. That is because Vedic hymns are associated with Devatas, Rishis, Chhanda and they have hidden sacrificial and spiritual symbols. So, the knowledge of trait of Devata and Rishis associated with them as well as the significance of rituals that hymns do imply and meters in which they are to be chanted is very important while interpreting Vedas.

As a part of Vedas, Brahmanas explains the sacrifices and rituals, Aaranyakas the subtle significance of them and Upanishads the spiritual knowledge. Ancient Vedic Sanskrit is different than common Sanskrit we use today and hence understanding the true meaning of Vedas is believed to be difficult task. This triggers the requirement of interpreting Vedas, many attempts have been made by Acharyas to interpret Vedas and some of them have written commentaries on Vedas also.

Yāska has mentioned following conventional/traditional schools or methods for interpretation of Vedas in his Nirukta:

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  Yājñikā

  
  
  

  This is the ritualistic or sacrificial method of interpretation. This is the most ancient and dominant school of interpretation. Example: Sayanacharya's Bhashya on Vedas follows the Yajnika school of interpretation.

  
  
  

  Mention of Yajnika school in Nirukta by Yaska 5.11:

  
  
  

  
  

  तत्र एतत् याज्ञिकाः वेदयन्ते ।
  यम् अक्षितिम् अक्षितयः पिबन्ति ।
  तानि एतस्मिन् काले एकेन प्रतिधानेन पिबन्ति ।
  तानि अत्र सरांसि उच्यन्ते ।
  त्रिंशत् अपरपक्षस्य अहोरात्राः ।
  त्रिंशत् पूर्वपक्षस्य इति नैरुक्ताः ।

  
  
  

  With reference to this, the interpretation of the ritualists is the following : There are thirty libation- vessels consecrated to one deity at the meridional pressing of the soma-juice. These (libation-vessels) they drink at a single draught. They are here called lakes. ' There are thirty days and nights in the second, and thirty in the first half of a month' say the etymologists.

  
  

  
  
  

  This school of interpretation is also mentioned at Nirukta 7.4, 7.23, 11.29, 13.9
  
  
  

  
  


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  Nairuktā

  
  
  This is the etymological school of interpretation which interprets Vedic words on the basis of their derivative connection. Yaska's Nirukta is itself the best example of this school . This schools is mentioned at Nirukta 1.12, 14, 2.8, 2.6, 3.8
  
  
  


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  Aaitihāsikā

  
  
  

  This is historical or mythological school of interpretation which tries to relate Vedic mantras with Itihasa and then interprets the Vedic hymns accordingly. This school follows the stories narrated in some Brahmanas to interpret Vedas.

  
  
  

  Mention of Aitihasika school in Nirukta 2.16:

  
  
  

  
  

  त्वाष्ट्रः असुरः इति ऐतिहासिकाः
  
  It's a demon of Tvasta, say the legenderians.
  
  
  

  
  

  
  


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  Parivrajaka

  
  
  

  This is a mystic school of interpretation according to which Vedic mantras can be interpreted to conform to their mystic ideas, e.g Mitra is interpreted as Prana and Varuna as Apana in prose portion of Brahmanas.

  
  
  

  Mention of this school in Nirukta 2.8:

  
  
  

  
  

  बहुप्रजाः कृच्छ्रम् आपद्यते इति परिव्राजकाः ।
  
  'People having many children fall into calamity' say the ascetics. 'It
  refers to the phenomenon of rain' say the etymologists.

  
  

  
  


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  Vaiyākaraṇā

  
  
  

  This is the grammarian school of interpretation according to which noun, verb, prepositions and particles are four measured division of speech. Patanjali's Mahabhashya is best example of this school of interpretation.

  
  
  

  Mention in Nirukta 9.5, 1.12:

  
  
  

  
  

  मण्डयतेः इति वैयाकरणाः ।
  
  It is derived from (the root) mund (to decorate),' say the grammarians.

  
  
  

  न सर्वाणि इति गार्ग्यः वैयाकरणानां च एके स्यात् ।
  
  'Not all" say Gargya and some of grammarians.
  
  
  

  
  

  
  


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  Naidānā

  
  
  

  This is school of interpretation done by those who are expert in nidānam i.e prime cause or correct diagnosis. Not much details I found on this school except mention by Yaska as follows.

  
  
  

  Mention in Nirukta 6.9 and 7.12:

  
  
  

  
  

  स्यालः आसन्नः संयोगेन इति नैदानाः ।
  
  syālaḥ āsannaḥ saṃyogena iti naidānāḥ ।

  
  
  

  ऋचा समं मेनः इति नैदानाः ।
  
  ṛcā samaṃ menaḥ iti naidānāḥ ।

  
  

  
  

Besides these major schools, there are also some minor schools/methods of interpretation e.g. Akhyatsamaya, Adhidaivata, Adhyatma mentioned in 13th chapter of Yaska's Nirukta

Source / Reference:

• Interpretation of Rigveda, chapter II Structure of Rigveda, a research thesis from Shodhaganga.




• A true interpretation of Vedas page no. 8 (124)




• The History and Principles of Vedic Interpretation by Ram Gopal. (Recommended for study purpose)




• Sanskrit Verses of Nirukta are quoted from Wikisource and English translation for the same from The Nighantu and the Nirukta by Yaska, Lakshman Sarup from Internet Archive.

Sanskrit Wikipedia page on Nirukta talks about these means of interpretation:

वेदार्थानुशीलनाय तदाऽनेकपक्षाः आसन् । येषां नामानि अनेन प्रकारेण प्रदत्तानि सन्ति -

(१) अधिदैवतः, (२) अध्यात्मः, (३) आख्यातसमयः (४) ऐतिहासिकाः, (५) नैदानाः, (६) नैरुक्ताः, (७) परिव्राजकाः, (८) याज्ञिकाश्च ।

IAST:

vedārthānuśīlanāya tadā'nekapakṣāḥ āsan । yeṣāṃ nāmāni anena prakāreṇa pradattāni santi -

(1) adhidaivataḥ, (2) adhyātmaḥ, (3) ākhyātasamayaḥ (4) aitihāsikāḥ, (5) naidānāḥ, (6) nairuktāḥ, (7) parivrājakāḥ, (8) yājñikāśca ।

Note: Nirukta Sanskrit text with Hindi translation is also available on Internet Archive