I never installed a patch before. I tried to install SUPEE-10975 from here. But it does fail with the following message:
$ ./PATCH_SUPEE-10975_CE_v1.9.3.3_v1-2018-11-27-09-17-33.sh
Checking if patch can be applied/reverted successfully...
ERROR: Patch can't be applied/reverted successfully.
checking file app/code/core/Mage/Adminhtml/Block/Customer/Group/Edit.php
checking file app/code/core/Mage/Adminhtml/Block/Newsletter/Template/Edit.php
checking file app/code/core/Mage/Adminhtml/controllers/Cms/BlockController.php
checking file app/code/core/Mage/Adminhtml/controllers/Customer/GroupController.php
checking file app/code/core/Mage/Adminhtml/controllers/SitemapController.php
checking file app/code/core/Mage/Adminhtml/controllers/System/BackupController.php
Hunk #1 succeeded at 358 (offset -11 lines).
checking file app/code/core/Mage/Captcha/Model/Observer.php
checking file app/code/core/Mage/Captcha/Model/Zend.php
checking file app/code/core/Mage/Captcha/etc/config.xml
checking file app/code/core/Mage/Catalog/Model/Api2/Product/Image/Rest/Admin/V1.php
checking file app/code/core/Mage/Catalog/Model/Product/Attribute/Media/Api.php
checking file app/code/core/Mage/Cms/Model/Wysiwyg/Images/Storage.php
Hunk #2 succeeded at 380 (offset -8 lines).
checking file app/code/core/Mage/Core/etc/config.xml
Hunk #1 FAILED at 28.
1 out of 3 hunks FAILED
checking file app/code/core/Mage/Core/sql/core_setup/upgrade-1.6.0.6.1.2-1.6.0.6.1.3.php
checking file app/code/core/Mage/Dataflow/Model/Convert/Container/Abstract.php
Hunk #1 FAILED at 55.
Hunk #2 FAILED at 140.
2 out of 2 hunks FAILED
checking file app/code/core/Mage/ImportExport/Model/Import/Entity/Customer.php
checking file app/code/core/Mage/ImportExport/Model/Import/Entity/Customer/Address.php
checking file app/code/core/Mage/Payment/etc/config.xml
checking file app/code/core/Mage/Payment/etc/system.xml
checking file app/code/core/Mage/Payment/sql/payment_setup/upgrade-1.6.0.0.1.1-1.6.0.0.1.2.php
checking file app/code/core/Mage/Sendfriend/Block/Send.php
checking file app/code/core/Mage/Wishlist/controllers/IndexController.php
checking file app/code/core/Zend/Controller/Request/Http.php
checking file app/design/adminhtml/default/default/template/cms/browser/content/files.phtml
checking file app/design/frontend/base/default/layout/captcha.xml
checking file app/design/frontend/base/default/template/wishlist/sharing.phtml
checking file app/design/frontend/rwd/default/layout/page.xml
Hunk #1 FAILED at 36.
1 out of 1 hunk FAILED
checking file app/design/frontend/rwd/default/template/sendfriend/send.phtml
checking file app/etc/modules/Mage_All.xml
checking file app/etc/modules/Mage_Captcha.xml
checking file app/locale/en_US/Mage_Wishlist.csv
The next patch would delete the file js/lib/jquery/jquery-1.12.0.js,
which does not exist! Assume -R? [n]
Apply anyway? [n]
Skipping patch.
1 out of 1 hunk ignored
The next patch would delete the file js/lib/jquery/jquery-1.12.0.min.js,
which does not exist! Assume -R? [n]
Apply anyway? [n]
Skipping patch.
1 out of 1 hunk ignored
The next patch would delete the file js/lib/jquery/jquery-1.12.0.min.map,
which does not exist! Assume -R? [n]
Apply anyway? [n]
Skipping patch.
1 out of 1 hunk ignored
checking file js/lib/jquery/jquery-1.12.1.js
checking file js/lib/jquery/jquery-1.12.1.min.js
checking file js/lib/jquery/jquery-1.12.1.min.map
What can I do to resolve this?