LVM spanning over multiple disks: What disk is a file on? Can I lose a drive without total loss

Lets say we have two physical drives, sda and sdb. Both are 100 Megs. I put them into VolumeGroup1 and create one 200 meg LogicalVolume1.
What would happen if I create a 150 meg file? Would 100 megs physically be on sda and 50 on sdb?

Correct (assuming the filesystem was empty before the file was created).

If so, what tells the OS that a piece of the file is on one drive, and another piece is on the other?

LVM tells the operating system that there is one single 200MB disk. The LVM part of the kernel (it comes in two parts, userspace management tools and kernel drivers) will then map what the operating system sees to physical locations/blocks on the disks.

What about drive failure? Assuming no RAID, if sdb fails, will all the data on sda be lost? Is there anyway to control what files are on what physical drives?

Yes, consider the data lost.

If you create smaller Logical Volumes then you can use the pvmove command to move them from disk to disk.

How do you generally manage LVM? Do you create one or two large Volume Groups then make partitions as it makes sense? Any other tips?

I tend to create large Volume Groups and then create Logical Volumes as needed. There is no need to fully allocate all the space in a Volume Group; allocate it when it is needed. It's easy to increase the size of a Logical Volume, and pretty much all modern filesystems can be easily grown, too.

I recommend creating one large whole-disk partition to contain the PV. Set the partition type to be "8e" (Linux LVM). The reason being that if the disk is moved to a different host in the future, it is obvious that the disk was used with LVM and could help prevent mistakes with the handling of the data.

A second reason for a whole-disk partition: if you run pvcreate /dev/sdX on a device that already has a partition table, the LVM will work correctly until a reboot, at which time the LVM drivers will have a hard time finding the PV. (The LVM drivers assume that if there is a partition table on a disk, the PV must be located within a partition.)