How can I access my iphoto library after installing Catalina?

iPhoto uses 32-bit code, that cannot run on Catalina, and there will be no update for iPhoto. It has been replaced in 2015 by Photos for Mac. If you follow the procedure described by Nile, you can open your iPhoto Libraries in Photos for Mac. This is described in more detail here: Updating from iPhoto to Photos for macOS – Apple Support

And here you can see, what the migrated iPhoto Library will look like in Photos: content and metadata from iPhoto and Aperture

The procedure will work, if you have been using iPhoto '11 or iPhoto '09. If your iPhoto Libraries are older, you have to prepare them on a Mac with an older system version, that will allow you to run the iPhoto Library upgrader tool: Using the iPhoto Library Upgrader tool - Apple Support

It is not possible to prepare older libraries for the migration to Photos on Catalina. This should have been done years ago, when iPhoto '11 came out.

Here are some user tips from Photos for Mac  User Tips that will help you in your transition from iPhoto to Photos:

Notes on Migrating an iPhoto Library from iPhoto to Photos for Mac - read first

Moments in Photos are the New Events.

External Editors in Photos Are Here

Photo Editing Extensions for Photos for Mac

Post 9/30/2018 Printing Options for Photos - Apple Community

Ordering Books and Calendars on a Mac that cannot be updated past El Capitan 

Use Project Extensions to order print products in Photos after September 30, 2018 - Apple Support

Create and order print products in Photos with Project Extensions - Apple Support

Launch Photos with the Option key held down, click on Other Library, and choose the iPhoto one.

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