The hard way
This workflow can be a pain. FCP can't migrate projects to AE seamlessly like Adobe Premiere, and since I've doggedly refused to adopt Premiere, I've been forced to manually re-create my edit in AE, either by exporting my FCP sequence in Uncompressed 10-bit* (for MiniDV projects), or importing the native clips into AE and setting in/out points (for file-based clips, e.g. from solid-state media). The first is restrictive and hogs hard drive space, the second can be enormously time consuming even for a short sequence.
*At home I have FCP 5, so no ProRes codecs.
The easy way
The alternative was a very good utility called Automatic Duck, which looks like it has recently been assimilated into Adobe. It transfers to and from FCP, AE along with Avid and other software too,
The easy & cheap way
Recently I found an excellent After Effects script from Popcorn Island called FCP2AE, and it does a good job converting FCP's XML export file into After Effects CS3, CS4 and CS5. I have tried a legacy version on AE CS3 and it worked well. Unfortunately I can only use After Effects 7 at home, for which this script is not compatible.
The easy & cheap way if you're stuck in the Dark Ages
Shortly thereafter I made an even more fabulous discovery -- a similar solution which is compatible with older software all the way back to After Effects 6.5 and Final Cut Pro 4. BasicFCPtoAE is an application that converts FCP's XML file into an After Effects script, which can then be run in AE and imports the edited sequence and all the native footage. It uses an earlier version of FCP's XML, so it cannot transfer transitions and effects, but if all you want is to get your straight cuts into AE without re-editing the whole sequence again, it is proper bone-fide awesome.
In fact if you're just after no-nonsense cuts, BasicFCPtoAE is actually better than the more modern FCP2AE. For the latter, the imported sequences and clips are structured in a hierarchy of folders, whereas for BasicFCPtoAE your After Effects project shows the sequence and the clips, that's all. Much simpler to navigate.