This is how it is normally done - by hand:

 

So, what was the big problem?
Why did the sewing machine take so long to invent?

Clocks, guns, mechanical looms, automata and mechanical music machines were in regular use by the early 1800's. Many of these devices are far more complex than the sewing machine.

 Early inventors realized that attempts to copy the hand process of sewing were inefficient. The need to pull the whole length of the thread through the cloth meant that short runs of thread had to be used. No, the thread has to be fed in from the working end of the stitch. A new way of sewing had to be invented.
On this side the thread feeds down from the bobbin On this side the thread is locked into the material.
The Eye Pointed Needle
  A sewing machine is a combination of several inventions all synchronized to carry out three tasks.  
1. The loop of thread has to be carried through the cloth. This is always done with the "eye pointed needle" which can withdraw to leave the loop under the cloth. 2. This loop has to be prevented from pulling back through the cloth. A chainstitch machine does this by passing the next loop through it. A lockstitch machine feeds a second thread through the loop. 3. The material has to be moved forward between each stitch. Almost all machines now use a "four-motion-feed" for this.