Welcome to Homeschooling!
We loved many parts of ADV. I hope you do too!
The Language Arts built into ADV:
*Bi-weekly copying of a scripture verse that is also memorized and goes with the Bible unit being studied. As far as I can tell copying good writing does help them learn how to write. This is an older method that isn't used so much in public schools today; so it might be new for both of you.
*History note booking: The note booking pages are included in the student sheets and have a place to draw or color a picture that goes with the history reading and some blank second grade lines for them to write a few sentences. Oral narration is your dd simply telling you some things that she remembers from the history that you read. Then she will write a few sentences that summarize what stands out the most to her in the reading about the note book page topic; for example, George Washington.
*Spelling: MFW recommends Rod and Staff Grade 2 spelling. It has a certain amount of phonics built into the work book spelling pages at the second grade level. I also highly recommend this spelling program. In your TM there are daily spaces on the grid marked 'spelling'; these boxes are to remind you to do the spelling each day.
*English: MFW recommends Primary Language Lessons for second grade. It is a more gentle introduction to the study of language, grammar, picture study, etc. It is based on Charlotte Mason methods. It does include dictation. Dictation is where you will read a sentence to your dd and she will do her best to write it down. I usually have them study it first, then read it, and then they write it. Primary Language Lessons is a beautiful study of the English language. I think many MFW users find that it stands on its own. The only change I make to it is I skip the grammar lessons in it and use a different program for grammar. The PLL book is not easy and has much to teach.
Book Basket: In the back of the ADV TM in the Appendix are listed hundreds of books in each individual TM. The books are broken down for each week to go with the topics being studied in the history. You can find many of them at your library. The idea is to check the books out and allow your dd to look at them each day for 15 - 20 minutes. I have modified book basket some for my individual children & home. My 8 & 6 like to look at the books or have me read them to them. My 10 year old is an avid reader and likes to read all of them. In my experience the looking at books does increase an interest in learning.
Reading: This is where your dd can read aloud to you and practice reading. In the back of the ADV TM is a book list for 2nd, 3rd, 4th, and I think even 5th grade. These books are listed in the very back of the book basket list and are intended to be used for them to read themselves; where as the book basket books they may just look at or have you read parts of those books to them. There are also a number of places to see literature book lists that can be bought or used to check out from a library. My oldest, when he did ADV for second grade, also read readers from Honey for the Heart (sold by MFW for MFW1 ~ extensive book list), Pathway Readers (sold by Rod and Staff ~ they have comprehension questions in the books), and Sonlight readers (they come with comprehension questions).
Reading Comprehension: Oral narration is a wonderful way to find out what they are learning. It really is simply your dd just telling you what she remembers. The MFW TMs encourage it for Bible, history, and science.
This type of learning is different than text book learning that is primarily used in schools. I know I enjoy teaching it much more than text books, and honestly I think my children learn more.