You would need to give a lot more information to give am accurate estimate. Assuming a basic deployment with nothing fancy and the admin is already familiar with solarwinds then you could be planned and deployed in a day. On the other hand I just migrated a very large customer off another server monitoring tool, lots of custom templates, lots of alert logic to consider, had to coordinate with several teams, and integrate with a few existing tools. We spent about 3 months on the project.
It's a small deployment. Approximately 30 web servers, less than 10 network devices, and a few other miscellaneous application servers. Less than 200 monitors. There is no existing tool and the admin has used Solarwinds but is not an expert.
If the web servers are all the same and a template is created how long to deploy on each server.
Assuming servers are already built and patched and you have all your service accounts in place already, sounds like a day if you use the out of the box alerting and templates. Over time your admin will definitely want to tweak things to suit the environment, but it typically takes people a bit to get a sense of what changes they want to make. Discovering that size of environment and then deploying the iis template should take under 30 minutes to do the whole place assuming your admin knows where to look.
Assuming you have a windows server with all patches and a SQL server already set up, the install will take all of 20 minutes (I call it "SolarWinds' patented 5-click yes-yes-yes-GO-done install" but it's not patented and our legal dept always starts chewing aspirin when I say it at SWUGs). If you have to build any of those components, YMMV.
Adding servers is also easy, assuming you have an accurate list of devices (either names, IP addresses, or an AD container with precisely the servers you want to monitor in it). If that's the case, it can be done in an hour or so. I once onboarded 4,000 devices in 3 hours - but I knew EXACTLY what I was adding (both at the device level and the sub-element like interfaces, disks, etc). If you have to scan, though (either scan a subnet, or give a seed router and let it walk your environment, etc), that'll take more time. Ditto if you need to then cherry pick through the results.
And the actual MONITORING - you know, actually knowing which applications, services, log messages, and the like you want to monitor - can once again take from minutes to months, depending on what you know when you start.
Finally, setting up your alerts - the trigger logic, the reset ("all better") logic, the trigger actions (reset the service, wait 5 min. If not better, restart the server. wait 5 min. If not better, cut ticket. wait 20 min. if not better, email manager, etc), the reset actions (send page saying "go back to bed", change ticket status to "reversed") and so on can also take some time to tune.
And if you are thinking "I'll just use the out-of-the-box alerts", please note that vendors (all of them, not just SolarWinds) include alerts the same way there's a casserole recipe on the back of the Lipton soup mix box. It's not a best practice, it's a sample to give you an idea of what COULD be done.