The short answer is, “you can’t”. SL is designed for community and communication, not for privacy. If you really want to be alone in a virtual world, download and install Open Sim software on your own computer and enjoy an isolated Second-Life type world all your very own.
On Line Visibility. Even though you can select an option for “only my friends can see my on line status”, and even though you can un-check the on-line visibility status for individual friends, there are always ways for people to find out if you are on line. For example, I can look you up in Search and send you an IM. If I don’t immediately get back the standard “BobsYourUncle Resident is off line. Your message will be stored and delivered later” message, I know that you are on line. Or, some viewers place a little statement in the profile, “Current status: ONLINE”. Or, I could look at one of your groups. The Member box of the group includes information about which group members are on line.
The only way to hide your on line status is to come on line as somebody else…in other words, to log on as an alt.
Preventing Intrusion. You can keep others out of land you own with banlines. Setting up banlines around your property prevents entry by everyone except named residents. However, they only extend up to 50 meters, so they aren’t much use if you live in a skybox. Also, many estates prohibit their use to enable free movement of other estate residents. You can put out a security orb to protect your property or a portion of it, like the inside of your home. These can be a pain sometimes…you invite a friend over, and ten seconds later she’s thrown off the property because you forgot to add her to the allowed list. There are also tools that let an intruder nullify the ejection function of the security orb.
In any case, while banlines and security systems prevent physical intrusion, they can’t keep someone from sitting outside your land and zooming their camera inside your house to watch you. Remember that local text chat has a range of 20 meters; if any avatar is closer to you than that, use IM to keep your conversation private. If you are using voice, a listener can move their camera close to you and hear you as if they were standing right there…so IM or a private voice call may be indicated here too.
Radars, such as those included in several third party viewers or in add-on gadgets like the MystiTool, are good for increasing your awareness of who is in the immediate area.
Skyboxes, located high up, are often a preferred style of residence. They’re a little harder to find, and usually experience less lag than ground level locations. If you enclose it in two counter-rotating hollow spheres, it gets a bit harder to move a spying camera inside. But the only way to really be private is to buy your own full private estate region, located at least one sim away from any other region, and set entry permissions for only yourself and your trusted friends. That’s expensive…an estate region will cost you $1,000 USD to buy, and $295 USD per month in tier.
The bottom line: if privacy is a serious concern…do it outside of SL.