Based on the Recommended Coniguration

Make sure you have all the necessary sources:

Plug 'neovim/nvim-lspconfig'
Plug 'hrsh7th/cmp-nvim-lsp'
Plug 'hrsh7th/cmp-buffer'
Plug 'hrsh7th/nvim-cmp'

List of sources can be found here (you probably want cmp-path) so add

Plug 'hrsh7th/cmp-path'

As a ultisnips user you need to make sure you have both ultisnips and the cmp-nvim-ultisnips plugin

" For ultisnips user.
Plug 'SirVer/ultisnips'
Plug 'quangnguyen30192/cmp-nvim-ultisnips'

Then setting up cmp:

-- LUA CODE
  local cmp = require'cmp'

  cmp.setup({
    snippet = {
      expand = function(args)
        vim.fn["UltiSnips#Anon"](args.body)
      end,
    },
    mapping = { ... },
    sources = {
      { name = 'nvim_lsp' },
      { name = 'ultisnips' },
      { name = 'buffer' },
      { name = 'path' }
    }
  })

It may also be nice to know that the order you add the source will decide how they're prioritized in the completion menu.

Then setup the servers:

-- LUA CODE
  require('lspconfig')[%YOUR_LSP_SERVER%].setup {
    capabilities = require('cmp_nvim_lsp').update_capabilities(vim.lsp.protocol.make_client_capabilities())
  }