Start by chaining a multiple of 4. I chained 16 for my swatch, but I would chain 20 or 24 for a scarf width depending on the yarn and hook size. Add 4 more chain stitches. Since I started with 16, this brings my total to 20.
We are now ready to begin the first row. The entire pattern will be worked as double crochet. Skip the first 3 chain stitches, yarn over, and insert your hook into the fourth chain stitch.
Work 1 double crochet stitch into each chain stitch across. I have 18 posts including the turning chain made by skipping those first three stitches.
Chain 2 and turn. We will now begin our second row by working around the posts. We will not be working into the "v's" like we would if we were doing another row of double crochet. We will be working around the posts made by the stitches of the previous row.
Skip the first post. Yarn over and insert your hook from right to left under the following double crochet stitch. In this picture you can see the post resting over the front of my hook, followed by my yarn over, followed by my working loop (the loop that always stays on your hook as you work).
Yarn over and draw up a loop just like you would with any other double crochet stitch.
Finish your double crochet stitch as you normally would (yarn over, pull through two, yarn over, pull through two again). Congratulations! You have made a front post double crochet stitch. Notice that the stitch is now raised in the front.
Work three more stitches in just the same way, inserting your hook under the posts.
We will now start a new set of four, this time back post double crochet. Yarn over and insert your hook from right to left under the next post from the back of the work. The post will rest on the back of your hook. Here you see a view from the top.
Here is a view from the front. Notice my hook is behind the work and the post of the current stitch is resting on the back of my hook.
Yarn over and draw up a loop.
You now have three loops on your hook. Finish the stitch just like a regular double crochet to complete your back post double crochet stitch.
Here I have completed 4 back post double crochet stitches, inserting my hook from behind each time, pulling the posts back. Notice the difference between the four front post stitches and the four back post stitches.
Here is a view from the top.
Remember those front post double crochet stitches? Work another set of four. Continue working alternating sets of four until you reach the end of the row. I worked 4 front post dcs, 4 back post dcs, 4 front post dcs, and 4 back post dcs.
To finish the row, work 1 double crochet stitch into the top of the turning chain from the previous row. Chain 2 and turn.
For row three simply repeat row two. In other words, when you come to a front post like the one above, work a front post double crochet stitch. When you come to a back post, work a back post double crochet stitch.
Here is my first completed front post stitch of my third row.
Remember to insert from the back when working a back post double crochet.
Draw up a loop.
Finish the stitch as you would a normal double crochet stitch.
Finish the row by working a double crochet stitch into the top of the turning chain as before.
Whew! We are done with row three, our second row of around the post crochet. Remember, our first row was regular double crochet.
Work two more rows as we did before. Here is my swatch at the end of my fifth row. I worked 1 row of regular double crochet and then 4 rows of around the post crochet.
Four our next row (row 6) we will start by chaining 2 as before.
Don't panic. We are going to reverse the position of our posts. Instead of starting with a front post double crochet, we will start with a back post double crochet. Here I have yarned over and inserted my hook from the back, pulling the first post back as well.
This is what it looks like from the front. Complete the stitch as you would a normal double crochet.
Here is a view from the back after I completed the stitch. Repeat this process for the following 3 front posts, converting them into back posts.
When you reach a back post, work a front post double crochet stitch, inserting your hook from the front. Here I have drawn up a loop before finishing the stitch.
This is what your work should look like at the end of row 6. The front posts are now back posts and vice versa. It may feel funny to work these stitch changes but I know you can do it! If you make a mistake simply pull it out and try again.
Don't forget to work 1 double crochet into the top of the turning chain at the end of every row. In this picture you can see the turning chain just hanging out and waiting to be crocheted into.
For rows 7, 8, and 9, go with the flow. When you reach a front post work a front post, when you reach a back post work a back post. Here I am at the end of row 9 after completing two sets of 4 rows each. To continue your object, continue working 4 rows alike and switching the posts on every 5th row. These sets of four identical rows are what form your basketweave.
If you have any questions, feel free to ask them in the comments! If you need a good video, I suggest All Free Crochet's YouTube series with Mikey. Happy hooking!