Hi,
I assume you did not draw a schematic. Did you?
--> I recommend to first draw a schematic ... then generate the board from the schematic data.
It seems you are drawing lines as with a pencil.. but this is not the way one does with a CAD software.
EAGLE is intelligent and helps you to route the signals more efficentely.
I recommend to go through the tutorials. Step by step.
*****
To your problem:
You see that the errors says S$18 and S$19.
You can use "show S$18" to highlight the signal.
The same for S$19.
A connection from one pin of one device to another pin to another device usually is shown by a "signal", at first it is a airwire in the "unrouted" layer.
Select "route". then select an airwire and EAGLE generates a trace from it. It shows you the start point and the end point.
Select a 45° wire angle (or ther trace bend mode with the right mouse key) and place the trace. you may choose another layer (witout leaving the "route" command) and automatically EAGLE generates the via at the right place.
Usually you don´t place the vias by hand.
Klaus