Assumes you have a developer account with apple – costs (as of 1-Nov-2017) £79 p.a.

From your target device head to https://developer.apple.com/download/ and download the iOS 11.2 profile.

or save to iCloud and access from ‘files’ on you iPhone

Read the release notes, note any concerns! – i.e. https://download.developer.apple.com/Documentation/Beta_Release_Notes_Oct_30_2017/iOS_11.2_beta_Release_Notes.pdf

If needed, notes on how to install – https://developer.apple.com/support/beta-software/install-ios-beta/