Multiplication Explanation
The following is an easy way to learn the times tables using number patterns.

Anything times 0 is 0
Anything times 1 is itself
Anything times 2 is double itself
Anything times 4 is double itself times 2 (double the 2's)
Anything times 5 ends in either a 0 or a 5, making it easy to count to your answer (5,10,15,20,25,30 etc.)
So far, these are the relatively easy numbers, but they leave only a handful of others, and many of them are easy also
Anything times 8 is double itself times 4. You can also count the 8 times numbers by remembering a neat little pattern: starting with 8, the next number increases the digit in the 10s column by 1 and decreases the digit in the 1's column by 2. Notice the pattern in this column of numbers.
08
16
24
32
40
48
56
64
72
80

9's are the next hardest one to learn, but you already know 9x0, 9x1, 9x2, 9x3, 9x4, 9x5, and 9x8, you're well on your way!
But the nines have several patterns you can use to learn them all directly. Similar to with the 8's. Starting with 9, the next number increases the digit in the 10s column by 1 and decreases the digit in the 1's column by 1:
09
18
27
36
45
54
63
72
81
90
Lesson Video 3 above explains a good hand trick to learn the 9's
You can also remember it this way: 9x# = #-1 in the tens column and 10-# in the ones column:

      (solve for         (solve for
      number in          number in
      tens column        ones column
      in answer)         in answer)     (answer)
9x# = #-1 = t            10-# = n     = tn

9x1 = 1-1 = 0            10-1 = 9     = 09

9x2 = 2-1 = 1            10-2 = 8     = 18

9x3 = 3-1 = 2            10-3 = 7     = 27

9x4 = 4-1 = 3            10-4 = 6     = 36

9x5 = 5-1 = 4            10-5 = 5     = 45

9x6 = 6-1 = 5            10-6 = 4     = 54

9x7 = 7-1 = 6            10-7 = 3     = 63

9x8 = 8-1 = 7            10-8 = 2     = 72

9x9 = 9-1 = 8            10-9 = 1     = 81

Learn to count by 3 to get the 3's. You already know 3x0, 3x1, 3x2, 3x4, 3x5, 3x8, and 3x9
Still, if you have trouble, it's not too difficult to count by 3. If you can count by 2, which is fairly easy, you can count by three, even if you have to think in your head:
1, 2, 3 4, 5, 6 7, 8, 9 10, 11, 12 13, 14, 15 16, 17, 18 19, 20, 21 22, 23, 24 25, 26, 27 28, 29, 30 31, 32, 33

To get the 6 times tables, just use every other 3. To get the higher numbers, you'll need to continue the pattern above. There are other ways to do it, but this is one easy way. Note that you already know several of the 6s from the above lessons.
1, 2, 3 4, 5, 6 7, 8, 9 10, 11, 12 13, 14, 15 16, 17, 18 19, 20, 21 22, 23, 24 25, 26, 27 28, 29, 30 31, 32, 33 34, 35, 36 37, 38, 39 40, 41, 42 43, 44, 45 46, 47, 48 49, 50, 51 52, 53, 54 55, 56, 57 58, 59, 60

7's are the hardest, but since you've done so well so far, there's great news! There's only one problem left not already covered. And that's 7x7. Many of these problems have rhymes to help you get the answer, which are reviewed elsewhere. However, there was no rhyme for 7x7 until I came up with one:
7 times 7 has no rhyme
you just have to remember
it's forty nine!

And with that folks, you have just learned all the times tables!