The Appropriations Committee reviews budget requests from the president, solicits testimony from government officials, and drafts funding legislation that gets reported to the full Senate. The Senate then works with the House to pass all appropriations bills by October 1, the beginning of the fiscal year.
For more detail on the process, read:
The Congressional Appropriations Process: An Introduction (pdf)
Tables list appropriations bills, hearings, and reports by fiscal year. For FY2017 and later years, tables will link to Congress.gov.