Technical support is one of the things that distinguishes a premium hosting provider from a cheap one.
A premium hosting provider will respond to your issues almost immediately and ensure all issues are followed up and resolved as quickly as possible. If an issue can't be resolved it is escalated until it can be. If it's related to an incident, an incident report may be sent to the customer within 24 hours. A job will only be closed once the customer approves.
A cheap hosting provider may wait a day or so before responding. And even then, it might be simply to seek further information about your issue. They might eventually resolve the issue but probably won't ask you if it's OK to close the job - they'll just close it.
A bad hosting provider might not even respond.
Of course, this is a generalization. Some cheap hosting companies are very quick at responding. But you need to be aware that, the less you pay, the greater the likelihood that the quality of the technical support will be lower.
Your technical support requirements will largely depend on how complex your website is. If you have a small, static website, you might only need to contact your hosting provider once or twice per year. If you have a more complex site or many sites, you may find yourself contacting your hosting provider on a weekly or even daily basis. This is especially true if the website is constantly changing with new "sub-sites" being added, or if you have multiple development projects occuring simultaneously.
Online Ticket Systems
Your hosting provider might offer multiple methods of contact. For example, they might offer phone support, live chat, email, or an online ticket system.
Many hosting providers require that all support requests are logged with the online ticket system. Doing this ensures that there is no confusion over what was actually requested, and what the response was. This can be particularly useful on long running requests, or if you need to refer to another support request. A ticket system can also be a great knowledgebase. This can be useful for both parties.
There's been a recent trend for hosting companies to discontinue their online ticket system, in favor of a chat system or phone support.
If an online ticket system is important to you, be sure to check for this when researching prospective hosting providers.
This can be easy to miss if you're not looking for it. These companies are unlikely to include "No Online Ticket Support!" in their advertising spiel.