It is essential to recite Birchas HaTorah with joy and gratitude for the privilege of engaging in Torah Study (Mishnah Berurah 47.4).
If one forgets to say Birchas HaTorah and remembers during Pesukei DeZimrah, they should recite them between the paragraphs (Mishnah Berurah 51.10).
However, suppose one only remembers during Brachos Kriyas Shema. In that case, it's advised not to interrupt but to have in mind to fulfill the obligation with Ahavat Olam and learn a bit after davening (Mishnah Berurah 52.9).
Suppose one forgets Birchas HaTorah before prayer and remembers afterward without learning immediately. In that case, one should not say the Bracha because there's a debate about whether or not he fulfilled his obligation during Ahava Raba (Shulchan Aruch 47.8).
When unsure about reciting the blessings, it's preferable to hear someone else say them; otherwise, intend to fulfill it with Ahavah Raba or Ahavas Olam and learn after prayer.
Ashkenazim may still say the "Asher Bacher Banu" blessing (Mishnah Berurah 47.1).
Writing Torah, even without reading, qualifies as learning and necessitates Birchas HaTorah if understanding is involved (Magen Avraham 47.1).
Due to disagreement, Ashkenazim typically avoid thinking of Torah before blessings, but performing a Mitzvah before blessings is permissible, even if it involves contemplating its laws (Mishnah Berurah 47.7).
Listening to Torah speeches, whether from a person or electronic device, requires blessings. While some allow interruptions between blessings and learning, avoiding such breaks is preferable. People often recite Parshas Birkas Kohanim immediately after the blessings (Shulchan Aruch 47.9).