I did this at a previous job, so here are a few tips for what will make it easier on everyone.

Plan at least 4, preferably 6, weeks out.

This gives your watch-standers the chance to arrange their lives around the schedule. At 6 weeks out, they'll be rearranging their lives around the schedule, rather than rearranging the watch-schedule around their lives. As the one managing the schedule, this means you'll be doing fewer weekend-swaps and people are more likely to just know who is on call.

Send out calendar events for the rotations.

This is more of a weekend-watch thing, but putting calender events in their calendar will further cement that they're obligated for that period. Also, it's a nice reminder in email (or whatever) that their shift has been scheduled.

Have the call list posted somewhere mobile-friendly.

Many times, the watch-stander is merely the first responder; it's their job to figure out what domain the problem sits in (app/database/storage/hypervisor/facilities/etc) and call the person who can actually fix the thingy. Having the call-list easily accessible from mobile is a really nice thing to have. This can be a Google Doc, or an app like PagerDuty. An Excel spreadsheet on Sharepoint is not so much.

Have the duties of the watch-stander clearly defined.

This seems obvious, but... it isn't. There are some questions you need answers to, otherwise you're going to experience sadness:

How fast must they respond to automated alerts?

Do they need to always answer the phone, or is voice-mail acceptable so long as the response is within a window?

How fast must they respond to emails?

The answers to these questions tell the watch-stander how much of a life they can fit in around the schedule. A movie is probably Right Out, but nipping out to the grocery store for a few things... maybe. Do they need to turn on bluetooth while driving, or can they wait until they stop (or just not drive at all)? How much 'response' can happen on a phone will greatly affect the quality-of-life questions.

What kind of sadness can you expect?

Missed alerts mostly. Without clearly defined response guidelines your watch-standers are going to sleep through their phones, miss emails, and otherwise fail to meet performance expectations. If you write those expectations down, they're far more likely to stick to them!

If you're doing automatic alert assignment, have an escalation policy.

You need a backstop in case the watch-stander sleeps through something. The backstop tier should never get called, but when they do it's an Event. An event people try to avoid, because something failed. Knowing that someone will notice if an automated alert gets ignored makes people more likely to respond in time.

If you're doing a 7-day watch, swap shifts on something other than Monday or Friday.

Depends on locality, but for US locations, Monday Holiday Law means that Mondays are occasionally vacation days and you don't want to do a watch-swap on a non-business day. In the same vein, many organizations have a rule in place stating that if the observed holiday in the case of an exempt holiday (New Years for example) lands on a Saturday is to have the day off be Friday.

At the same time, there is a US holiday that camps on top of Thursday (see next item). Tuesday or Wednesday are good choices.

If you're doing a weekend watch, have a policy in place for handling long weekends.

The 4 day Thanksgiving Holiday in the US is a great example, as that duty schedule is double what a normal one would be. Decide if you're going to create two shifts for it or allow one person to cover the whole thing, and decide well in advance. For some organizations the Friday after Thanksgiving is a major production day so this may be moot ;).