GitLab's REST API lives at https://gitlab.com/api/v4 (or your self-managed host). Projects are addressed by numeric id or URL-encoded path, e.g. gitlab-org%2Fgitlab.
Public projects can be read without a token. For private data, create a personal access token under Access tokens and send it as the PRIVATE-TOKEN header. In the examples it's written {{GITLAB_TOKEN}}.
Full reference: https://docs.gitlab.com/api/rest/
No token needed for public projects.
curl https://gitlab.com/api/v4/projects/gitlab-org%2Fgitlab
curl https://gitlab.com/api/v4/user \
-H "PRIVATE-TOKEN: {{GITLAB_TOKEN}}"
curl "https://gitlab.com/api/v4/issues?state=opened&scope=assigned_to_me" \
-H "PRIVATE-TOKEN: {{GITLAB_TOKEN}}"
curl "https://gitlab.com/api/v4/projects/{{PROJECT_ID}}/pipelines?per_page=5" \
-H "PRIVATE-TOKEN: {{GITLAB_TOKEN}}"