As long as you're logged in to your Google account, creating new reminders or appointments on your calendar is as easy as visiting the Google homepage and typing into the search bar. You don't have to open reminders specifically, or go right to your calendar -- Google will handle the rest.
Google Operating System explains how this works. All you have to go is visit Google and, for reminders, type
add reminder or
create reminder into the search bar, and the interface will change to let you fill in the details. For reminders, you'll get a field asking what you'd like to be reminded of, when, and where. You can even click to have Google Now remind you on your mobile device. If you type in more details from the start, like "add reminder to call Whitson tomorrow", the fields for when and what will fill themselves in automatically.
For calendar events, type
add meeting, or
schedule appointment into the search bar. From there, you'll get a default appointment for the next half-hour, all set to go. You can either click "create event" to add it to the calendar as-is, or click the time to go to Google Calendar and edit the specifics. Even if you click "create event", you'll then get a link to edit the event once it's been added. Again, if you add more specifics, like "create event for Thursday at 11am: Call Whitson", Google will fill in the rest for you and you can just add the appointment to your calendar, no additional editing required.
The nice thing about these tricks is that they work on the desktop in any browser you use, right from the Google Search box. If you're using Chrome and have voice input enabled, they will work using your voice as well. Hit the links below for more examples.
Create Google Calendar Events in Google Search [Google Operating System]
Create Reminders in Google Search [Google Operating System]