For a simple two-sided board, start by creating a ground polygon on the whole bottom layer. The trick then is to get Eagle to route most of the connections on the top layer. To do this, make the cost of routing within a polygon high and the via cost low. Actually you want to start with parameters more likely to find a solution, then tighten up the requirements over multiple optimization passes.
Before auto-routing, route the critical traces manually, and connect any grounds you can right at the pad to the ground layer. That will cause it not to waste routing space connecting the grounds.
Of course this all has to start with good layout that tries to put connected things near each other and oriented to have as few crossovers as possible.
After the auto-routing, you have to do some manual cleanup. The measure of a ground plane is how small the maximum dimension is of any island. Lots of small islands are better than a few big ones. This means you want the ground plane to flow around every via if possible. Unfortunately Eagle tends to clump vias, even with the hugging parameter set to 0. You can't set it negative, I tried. This means you have to see what the auto-router did and move things around a little to try to break up clumps of vias.
It's mostly about using the auto-router properly and realizing it's a tool, not a substitute for your own brain. If you are expecting fire and forget, you aren't going to get good boards.
Anyway, here is a auto-router control file from one of my 2 layer boards with the bottom layer a ground plane:
[Default]
RoutingGrid = 4mil
; Trace Parameters:
tpViaShape = Round
; Preferred Directions:
PrefDir.1 = *
PrefDir.2 = 0
PrefDir.3 = 0
PrefDir.4 = 0
PrefDir.5 = 0
PrefDir.6 = 0
PrefDir.7 = 0
PrefDir.8 = 0
PrefDir.9 = 0
PrefDir.10 = 0
PrefDir.11 = 0
PrefDir.12 = 0
PrefDir.13 = 0
PrefDir.14 = 0
PrefDir.15 = 0
PrefDir.16 = *
Active = 1
; Cost Factors:
cfVia = 50
cfNonPref = 5
cfChangeDir = 2
cfOrthStep = 2
cfDiagStep = 3
cfExtdStep = 0
cfBonusStep = 1
cfMalusStep = 1
cfPadImpact = 4
cfSmdImpact = 4
cfBusImpact = 0
cfHugging = 3
cfAvoid = 4
cfPolygon = 10
cfBase.1 = 0
cfBase.2 = 1
cfBase.3 = 1
cfBase.4 = 1
cfBase.5 = 1
cfBase.6 = 1
cfBase.7 = 1
cfBase.8 = 1
cfBase.9 = 1
cfBase.10 = 1
cfBase.11 = 1
cfBase.12 = 1
cfBase.13 = 1
cfBase.14 = 1
cfBase.15 = 1
cfBase.16 = 5
; Maximum Number of...:
mnVias = 20
mnSegments = 9999
mnExtdSteps = 9999
mnRipupLevel = 50
mnRipupSteps = 300
mnRipupTotal = 500
[Follow-me]
@Route
Active = 1
cfVia = 8
cfBase.16 = 0
mnRipupLevel = 10
mnRipupSteps = 100
mnRipupTotal = 100
[Busses]
@Route
Active = 1
cfVia = 10
cfChangeDir = 5
cfBusImpact = 4
cfPolygon = 25
cfBase.16 = 10
mnVias = 0
mnRipupLevel = 10
mnRipupSteps = 100
mnRipupTotal = 100
[Route]
@Default
Active = 1
[Optimize1]
@Route
Active = 1
cfVia = 99
cfNonPref = 4
cfChangeDir = 4
cfExtdStep = 1
cfHugging = 1
cfPolygon = 30
cfBase.16 = 10
mnExtdSteps = 20
mnRipupLevel = 0
mnRipupSteps = 100
mnRipupTotal = 100
[Optimize2]
@Optimize1
Active = 1
cfNonPref = 3
cfChangeDir = 3
cfBonusStep = 2
cfMalusStep = 2
cfPadImpact = 2
cfSmdImpact = 2
cfHugging = 0
cfPolygon = 40
mnExtdSteps = 15
[Optimize3]
@Optimize2
Active = 1
cfVia = 80
cfNonPref = 2
cfChangeDir = 2
cfPadImpact = 0
cfSmdImpact = 0
cfPolygon = 50
mnExtdSteps = 10
[Optimize4]
@Optimize3
Active = 1
cfVia = 60
cfNonPref = 1
cfPolygon = 60
cfBase.16 = 12
[Optimize5]
@Optimize4
Active = 1
cfVia = 40
cfNonPref = 0
cfPolygon = 70
cfBase.16 = 14
mnExtdSteps = 5
[Optimize6]
@Optimize5
Active = 1
cfVia = 20
cfBase.16 = 16
[Optimize7]
@Optimize6
Active = 1
cfBase.16 = 18
[Optimize8]
@Optimize7
Active = 1
cfBase.16 = 20
Best Answer
Your bottom ground plane doesn't fill because you have two SMD parts, so filling it would not create any connections! If you put it on the top layer (simply select the top layer from the drop down menu after clicking the polygon tool), all required connections can be created. In case you want to use the bottom layer as GND, you need to create vias.