A domain is a list of criteria, each criterion being a triple (either a list or a tuple) of (field_name, operator, value)

So in your example, like this:

[   ('employee_id', '=', [1])   ]

For example, this code:

#!/usr/bin/env python
# coding: utf-8

import xmlrpclib 

dbname = '246626-10-0-928fbd-all' 
username = 'admin' 
pwd = 'admin' 

sock_common = xmlrpclib.ServerProxy('http://246626-10-0-928fbd.runbot8.odoo.com/xmlrpc/common') 
sock = xmlrpclib.ServerProxy('http://246626-10-0-928fbd.runbot8.odoo.com/xmlrpc/object') 

uid = sock_common.login(dbname, username, pwd) 

timesheet_ids = sock.execute(dbname, uid, pwd, 'hr_timesheet_sheet.sheet', 'search_read', 
                             [('employee_id', '=', [1])]) 

if timesheet_ids: 
    print 'employee 1 returned: %s\n\n' % str(timesheet_ids) 
else: 
    print 'employee 1 not found\n\n' 

timesheet_ids = sock.execute(dbname, uid, pwd, 'hr_timesheet_sheet.sheet', 'search_read', 
                             [('employee_id', '=', [987654321])]) 

if timesheet_ids: 
    print 'employee 987654321 returned: %s\n\n' % str(timesheet_ids) 
else: 
    print 'employee 987654321 not found\n\n'

Prints this:

employee 1 returned: [{'message_follower_ids': [3378], 'timesheet_ids': [35, 32, 31, 39], 
                       'create_date': '2017-07-18 19:10:52', 'attendance_count': 0, 
                       'message_needaction': False, 'message_channel_ids': [], 
                       'message_partner_ids': [3], 'attendances_ids': [], 
                       'write_uid': [1, 'Administrator'], 'id': 3, 
                       'create_uid': [1, 'Administrator'], 'employee_id': [1, 'Pieter Parker'], 
                       'user_id': [1, 'Administrator'], 'message_is_follower': True, 
                       '__last_update': '2017-07-18 19:11:10', 'date_from': '2017-07-17', 
                       'message_last_post': False, 'company_id': False, 'period_ids': [31, 35], 
                       'message_ids': [6421, 6420, 6419], 'state': 'draft', 
                       'message_unread_counter': 0, 'department_id': [3, 'Management'], 
                       'total_attendance': 0.0, 'account_ids': [35, 40, 31, 41, 37, 39], 
                       'write_date': '2017-07-18 19:11:10', 'date_to': '2017-07-23', 
                       'display_name': 'Week 29', 'total_difference': -22.0, 
                       'name': False, 'total_timesheet': 22.0, 'message_unread': False, 
                       'message_needaction_counter': 0}]





employee 987654321 not found

More at 

https://www.odoo.com/documentation/10.0/reference/orm.html#reference-orm-domains