After initial inquiry in a Zotero forum thread, and some trial-and-error, I was able to build the Zotero Standalone client from source using the bash scriptlet shown below). The main things I needed to learn were:

1. Location of the source: https://www.zotero.org/svn/standalone/trunk/
2. Location of build script: the root directory of the source contains the build_sa bash script
3. Build prerequisites
   1. Tools: subversion, bash and perl
   2. Non-source inputs: XULRunner. build_sa mentions a requirement for XULRunner runtime 2.0.*. However, Ubuntu does not package a 2.x XULRunner before 11.04, which is currently pre-release. For now, Pre-release xulrunner-2.x runtimes can be obtained from http://ftp.mozilla.org/pub/mozilla.org/xulrunner/nightly/latest-trunk/. build_sa states implicitly that it requires separate runtimes for each target architecture, and expects to find each such runtime in a directory with a conventional name (see bash scriptlet below).
4. Build control: build_sa uses no config file, takes no arguments, and is non-interactive. build_sa will build one or more of the target OSs (linux, mac or win32), but it decides which architectures are built for each.
5. Location of the build: ${BUILD_PATH}/Zotero_${BUILD_ARCH}/zotero (found with ls -alt ${BUILD_PATH} $(find -executable -type f) | grep -ve '.so$').

I automated a build on 64-bit Ubuntu with the following bash scriptlet:

START="$(date)"
# edit following vars as desired for your build
DOWNLOAD_ROOT="/tmp/xulrunner"
BUILD_ARCH="linux-x86_64"
BUILD_ROOT="${HOME}/bin/zotero/standalone"
BUILD_DIR="20101228"
BUILD_PATH="${BUILD_ROOT}/${BUILD_DIR}"
BUILD_SCRIPT="build_sa"
BUILD_SCRIPT_BAK="${BUILD_SCRIPT}.0"
XULR_SOURCE_ROOT="http://ftp.mozilla.org/pub/mozilla.org/xulrunner/nightly/latest-trunk"
XULR_TARGET_PATH="${BUILD_PATH}/xulrunner_${BUILD_ARCH}"
XULR_VERSION="2.0b9pre.en-US"
XULR_CHECKSUMS_NAME="xulrunner-${XULR_VERSION}.${BUILD_ARCH}.checksums"
XULR_CHECKSUMS_SOURCE="${XULR_SOURCE_ROOT}/${XULR_CHECKSUMS_NAME}"
XULR_CHECKSUMS_TARGET="${DOWNLOAD_ROOT}/${XULR_CHECKSUMS_NAME}"
XULR_ARCHIVE_NAME="xulrunner-${XULR_VERSION}.${BUILD_ARCH}.tar.bz2"
XULR_ARCHIVE_SOURCE="${XULR_SOURCE_ROOT}/${XULR_ARCHIVE_NAME}"
XULR_ARCHIVE_TARGET="${DOWNLOAD_ROOT}/${XULR_ARCHIVE_NAME}"
ZOTERO_SOURCE_ROOT="https://www.zotero.org/svn/standalone/trunk/"
ZOTERO_TARGET_EXEC="${BUILD_PATH}/Zotero_${BUILD_ARCH}/zotero"

# setup xulrunner
# download xulrunner
mkdir -p ${DOWNLOAD_ROOT}
wget -O ${XULR_CHECKSUMS_TARGET} ${XULR_CHECKSUMS_SOURCE}
wget -O ${XULR_ARCHIVE_TARGET} ${XULR_ARCHIVE_SOURCE}
# verify xulrunner
pushd ${DOWNLOAD_ROOT}
# sha512sum -c < ${XULR_CHECKSUMS_TARGET}
# fails with
# > sha512sum: standard input: no properly formatted SHA512 checksum lines found
# I tried (offline) some other invocations, which similarly all failed
# $ sha512sum -c < /tmp/xulrunner/xulrunner-2.0b9pre.en-US.linux-x86_64.checksums 
# sha512sum: standard input: no properly formatted SHA512 checksum lines found
# $ pushd ${DOWNLOAD_ROOT}
# $ sha512sum -c < ${XULR_CHECKSUMS_NAME}
# sha512sum: standard input: no properly formatted SHA512 checksum lines found
# $ sha512sum -c < xulrunner-2.0b9pre.en-US.linux-x86_64.checksums 
# sha512sum: standard input: no properly formatted SHA512 checksum lines found
# $ sha512sum -c xulrunner-2.0b9pre.en-US.linux-x86_64.checksums 
# sha512sum: xulrunner-2.0b9pre.en-US.linux-x86_64.checksums: no properly formatted SHA512 checksum lines found
# unpack xulrunner
tar xjf ${XULR_ARCHIVE_NAME}
mkdir -p ${BUILD_PATH}
# ASSERT: archives expand to ./xulrunner
mv ./xulrunner ${XULR_TARGET_PATH}
popd

# setup sources, including script
# checkout sources
pushd ${BUILD_ROOT}
svn co ${ZOTERO_SOURCE_ROOT} ${BUILD_DIR}
popd
pushd ${BUILD_PATH}
# backup unhacked build script
cp ${BUILD_SCRIPT} ${BUILD_SCRIPT_BAK}
chmod 444 ${BUILD_SCRIPT_BAK}
# hack build script to build only linux
chmod 755 ${BUILD_SCRIPT}
sed -si 's/BUILD_MAC=1/BUILD_MAC=0/g' ${BUILD_SCRIPT}
sed -si 's/BUILD_WIN32=1/BUILD_WIN32=0/g' ${BUILD_SCRIPT}
sed -si 's/BUILD_LINUX=0/BUILD_LINUX=1/g' ${BUILD_SCRIPT}
diff -u ${BUILD_SCRIPT_BAK} ${BUILD_SCRIPT}

# CHECK: you should see stdout like
# --- build_sa.0  2010-12-28 16:45:21.000000000 -0500
# +++ build_sa    2010-12-28 16:45:21.000000000 -0500
# @@ -1,7 +1,7 @@
#  #!/bin/bash
# -BUILD_MAC=1
# +BUILD_MAC=0
#  BUILD_WIN32=0
# -BUILD_LINUX=0
# +BUILD_LINUX=1

# build
BUILD_START="$(date)"
./${BUILD_SCRIPT}
echo -e "build   end=$(date)"
echo -e "build start=${BUILD_START}"

# run the built sa
${ZOTERO_TARGET_EXEC} &
echo -e "  end=$(date)"
echo -e "start=${START}"

The (penultimate) build step produced the output

Getting latest Zotero revision
Got Zotero r7528
Building translators.zip
Building styles.zip
Retrieving Zotero OpenOffice.org Integration
Building Zotero_linux-i686
# several errors here, as I did not have the xulrunner for this arch
Building Zotero_linux-x86_64

The run step puts up a Zotero window similar to that normally seen in Firefox. When initially run separately from the terminal, it produced the output

$ ./Zotero_linux-x86_64/zotero &
ERROR: There is no such extension deployed: org.Zotero.integration.openoffice
unopkg failed.

but I have not observed that subsequently.

Unfortunately I don't currently know how to test the build (much less on how to use it with Chrome) aside from the following smoketest: if I

1. Run the executable (e.g., ${ZOTERO_TARGET_EXEC}, ./Zotero_linux-x86_64/zotero).
2. Wait for the Zotero window, then select “Zotero Quick Start” in the center column.
3. Hit button=View in the right column.

a browser launches and and opens the quick start guide. That's comforting, but I'd prefer to know:

1. Is there a more extensive test suite? E.g., what do the Zotero development team do pre-commit?
2. How to load up my own (backed up) Zotero data (from my Firefox profile, or wherever else it might be) and do actual work?