You need to do a form submit and then do what you want with the submitted values.

Form template example: 

<form method="post"
	  class="s_website_form"
	  action="/routing-value"
	  enctype="multipart/form-data">
	<input type="hidden" name="csrf_token" t-att-value="request.csrf_token()"/>
	<div style="float: right;">
		<!-- html form input fields -->
		<select name="group_selection" style="padding: 3px;">
			<t t-foreach="selection_options" t-as="option">
				<t t-raw="option"/>
			</t>
		</select>
		<button type="submit" class="btn btn-primary">Show</button>
	</div>
</form>

Controller example

from odoo import http, _
from odoo.http import request
import odoo.addons.web.controllers.main

@http.route('/routing-value', type='http', auth='user', website=True)
def get_form_values(self, **kwargs):
	if request.httprequest.method == 'POST':
		selection_value = request.params.get('group_selection')
		user_id = http.request.env.context.get('uid')
                user = request.env['res.users'].search([('id', '=', user_id)])[0]
		# DO STUFF WITH THE GOTTEN DATA