BhG 3.19

syntax

tasmāt (therefore) asaktaḥ (unattached) [san] (being) satatam (constantly) kāryam (what is to be done) karma (activity) samācara (perform).
asaktaḥ hi (indeed unattached) karma (activity) ācaran (while performing) pūruṣaḥ (a person) param (the supreme) āpnoti (he obtains).

grammar

tasmāt	–	av. – therefore (from: tat sn. 5n.1 m. – from that);
asaktaḥ	–	a-sakta (√sañj – to attach, to stick, to embrace) PP 1n.1 m. – unattached;
satatam	–	av. – constantly (from: sa-tata – constant, uninterrupted);
kāryam	–	kārya (√kṛ – to do) PF 2n.1 n. – to be done, work, duty, especially religious one;
karma	–	karman 1n.1 n. – activity (from: √kṛ – to do);
samācara	–	sam-ā-√car (to behave, to perform) Imperat. P 2v.1 – you must perform;
asaktaḥ	–	a-sakta (√sañj – to attach, to stick, to embrace) PP 1n.1 m. – unattached;
hi	–	av. – because, just, indeed, surely;
ācaran	–	ācarant (ā-√car – to behave, to perform) PPr 1n.1 m. – [while] performing;
karma	–	karman 2n.1 n. – activity (from: √kṛ – to do);
param	–	para 2n.1 n. – beyond, ancient, final, the best, the supreme;
āpnoti	–	√āp (to obtain) Praes. P 1v.1 – he obtains, he achieves;
pūruṣaḥ	–	pūruṣa 1n.1 m. – a person (from: √pur – to precede, to lead or √pṝ – to fill, to nourish, puru – abundance, pūru – people, puruṣa – a person);

textual variants

samācara → samācaraḥ / samācaret (performing / he would perform);
param āpnoti → paraṁ prāpnoti (the supreme he obtains);
pūruṣaḥ → pūruṣam (Pūruṣa);

Śāṃkara

The key:
an excerpt from the commented verse
quotes from the scriptures
starting polemic

Wherefore:		yataḥ evaṃ —
Therefore, without attachment, constantly perform the action which should be done; for, performing action without attachment, man reaches the Supreme.		tasmād asaktaḥ satataṃ kāryaṃ karma samācara | asakto hy ācaran karma param āpnoti pūruṣaḥ ||3.19||
Performing action, without attachment, for the sake of the Īśvara, man attains moksha, through attaining purity of mind (sattva-śuddhi).		tasmāt asaktaḥ saṅgavarjitaḥ satataṃ sarvadā kāryaṃ kartavyaṃ nityaṃ karma samācara nirvartaya | asakto hi yasmāt samācaran īśvarārthaṃ karma kurvan paraṃ mokṣam āpnoti pūruṣaḥ sattva-śuddhi-dvāreṇa ity arthaḥ ||3.19||

Rāmānuja

yasmād asādhanāyattātmadarśanasyaiva sādhanāpravṛttiḥ, yasmāc ca sādhane pravṛttasyāpi suśakatvāc ca apramādatvād antargatātmayāthātmyānusandhānatvāc ca jñānayogino ‚pi mātrayā karmānuvṛttyapekṣatvāc ca karmayoga evātmadarśananirvṛttau śreyān, tasmād asaṅgapūrvakaṃ kāryam ity eva satataṃ yāvadātmaprāpti karmaiva samācara / asaktaḥ, kāryam iti vakṣyamāṇākartṛtvānusandhānapūrvakaṃ ca karmācaran puruṣaḥ karmayogenaiva param āpnoti ātmānaṃ prāpnotītyarthaḥ

Śrīdhara

yasmād evambhūtasya jñānina eva karmānupayogo nānyasya tasmāt tvaṃ karma kurv ity āha tasmād iti | asaktaḥ phala-saṅga-rahitaḥ san kāryam avaśya-kartavyatayā vihitaṃ nityaṃ naimittikaṃ karma samyag ācara | hi yasmād asaktaḥ karmācaran puruṣaḥ paraṃ mokṣaṃ citta-śuddhi-jñāna-dvārā prāpnoti

Madhusūdana

yasmān na tvam evaṃbhūto jñānī kintu karmādhikṛta eva mumukṣuḥ | asaktaḥ phala-kāmanā-rahitaḥ satataṃ sarvadā na tu kadācit kāryam avaśya-kartavyaṃ yāvaj-jīvādi-śruti-coditaṃ tam etaṃ vedānuvacanena brāhmaṇā vividiṣanti yajñena dānena tapasānāśakena iti śrutyā jñāne viniyuktaṃ karma nitya-naimittika-lakṣaṇaṃ samyag ācara yathā-śāstraṃ nirvartaya | asakto hi yasmād ācarann īśvarārthaṃ karma kurvan sattva-śuddhi-jñāna-prāpti-dvāreṇa paraṃ mokṣam āpnoti pūruṣaḥ puruṣaḥ sa eva sat-puruṣo nānya ity abhiprāyaḥ

Viśvanātha

tasmāt tava jñāna-bhūmikārohaṇe nāsti yogyatā | kāmya-karmaṇi tu sad-vivekavatas tava naivādhikāraḥ | tasmāt niṣkāma-karmaiva kurv ity āha tasmād iti | kāryam avaśya-kartavyatvena vihitaṃ paraṃ mokṣam

Baladeva

yasmāl labdhātmāvalokanasyaiva karmānupayogas tasmād etādṛktvaṃ kāryaṃ kartavyatvena vihitaṃ karma samācara | asaktaḥ phalecchā-śūnyaḥ san | paraṃ dehādi-bhinnam ātmānam āpnoty avalokate yāthātmyena