There's a lot they can do. Lobbyist at a minimum have the same access to a politician as you do. They can make phone calls, send letters, attend and speak at legislative hearings, or try to be involved in the right social circles. Building this social element is important for their continued success and gives them access beyond what a typical person could normally obtain.

More importantly they have influence because some group has a moneyed interest in legislation. This can give them the resources to do the above regularly. They might hire legal counsel to sue governments. They may be able to lend support to pet projects and gain support for their own goals.

I always assumed there was a lot of talking. Most politicians are inclined to want to help businesses anyway, as they provide jobs and generate tax revenue. If the lobbyist can come in and say “here’s what the cell phone providers nationwide need to stay in business and continue to generate good returns to shareholders and low prices to customers,” then that’s a powerful message - especially when the counter-argument is a pile of faxes and postcards from constituents that don’t tell a coherent story.

The money certainly doesn’t hurt, though.

They organize ways for their clients to bundle significant financial contributions to politician's campaigns so that when they "talk", they can point to significant past contributions or promise future contributions. Or threaten contributions to challengers.

Although individual contributions are limited in theory, bundling allows vast contributions in practice. For example, a CEO can persuade senior execs to donate the maximum to a candidate. Or someone can host a fundraiser at their home (or wine cave) and "encourage" many acquaintances to attend. They get credit with the politician for the total raised.

Finally, Political Action Committees can take unlimited contributions from anyone so long as they don't "coordinate" with a politician's campaign. In practice they can of course be very helpful to a candidate's campaign, and lobbyists will use that to influence.