IP Geolocation

Best way? That depends on your needs. There are various APIs (some free) that you send the IP to and they return the approximate location. These would be fine for casual/light usage. If you need to do heavy work then you may be best to pull bulk geoip data down periodically into your own database and serve it out from there.

The thing to note about location based on IP is that the accuracy can range from very accurate to very inaccurate depening on many different factors and it's practically impossible to know in advance whether the result will be accurate or not! Using HTML5 geolocation (providing the client enables it) should offer better accuracy as it does not rely on IP address alone.

How to display a map with multiple markers has already been answered and IP Geolocation is out of the scope of OSM (and there are multiple possibilities like a simple geoip database and the HTML5 geolocation feature).

HTML5 geolocation provides you higher accuracy compare to IP geolocation, but, the drawbacks is, permission need to be explicitly granted from the end user for solution.

Getting location information from IP will be less intrusive and seamless way with a little bit trade off on the accuracy. Anyway, it's depend on the the nature of your solutions.

Anyway, both solution above shall provide you the latitude and longitude information enabling you to plot the marker in your map.

If you need information on the differences between these 2, this site shall be able to give you some idea: ipgeo5.com and ipinfodb.com

Yes, you can use free IP geolocation API that provides point coordinates based on the IP address.

There are tonnes of IP geolocation APIs which can do the job. Try BigDataCloud's IP geolocation API which provides not just the coordinates of the IP address but also the area where the IP address might have been allocated. This is unique data that might be helpful.

They provide 10K queries per month for free and can be upgraded at a nominal feed.

Another provider that provides you with a really extensive and free dataset is https://ipbase.com.