Missions & Complexes

Have your ship(s) shipped via black frog to an NPC station of your choice. Take a cloaky from High to the Null Sec station.

Alternatively ship via black frog to a NPC station that has a medical facility and transfer you clone there, then pod yourself. (or if you can use jump clones)

Assuming you don't have sov and are trying to do this without friends.
The safest way would to have an online pos in an npc nullsec and leave an alt offline that is trained to cyno 5 in a covert ops in pos. Use a blops to either bridge in your a toon with a cov ops ship or bridge in the blops. have a ship hangar array and a corporate or personal hangar array to store your ships,ammo,and fittings.

But this method requires at least two accounts and you're going to want a jump freighter to move fuel and since a cyno can't be activated in a pos, this can expose your jump freighter to attack if not done correctly.

Easiest way would be to have a jump clone at a NPC station with your stuff stored in the station. However these systems tend to be populated and if you're not blue to the local's, you'll have fun trying to get away from the undock if they are camping the station. Items such as ship hulls can be hard to find on the market and typically are quite expensive compared to highsec markets.

If you have balls of steel, scout ahead with an alt, fit a mjd to the battleship hull and pray.

If you have a friend or a second char just scout you in.

Highsec <-> Null gates are often camped. The Backdoor though a lowsec gate might do the trick.
Take a look at the system in the map. Where there many kills in the last 24h?
MWD cloak trick can help in lowsec.
Use a very fast and cheap frig to make pounce/bounce/on-grid spots on important gates that are often camped. That way it's harder for the enemies to get you into a drag bubble.

Depends on how much isk and accounts you have.
Cheapest\easiest would probably be a T3 with covops and nullifies sub to get you to an NPC station, then refit. Helps to have another account to scout though.

Another option is to have a second account go out in a cloaky frig\bomber with a covert ops cyno and run the sites in a blops.. Sin works very nicely for this. Use covert ops so the cycno doesn't show up in the overview and has a short cycle.

Another option is to use a carrier, jump to destination with the aid of a second character and live out of the carrier till you want to head home. I did this for a while but with 3 characters. Only logged the carrier on to switch or move ships.. there are many very quite null places out there.
Best already has been suggested.. join a null corp/alliance. Suggest even doing this just to learn how to survive in null if you not familiar with living there.

Wow, lots of answers all across the board. Most bad, but that's just my opinion.

You want to get directly there without joining a renter or member corp to a large alliance, sinking a CRAPton of isk into a tower that you hope to get into npc null (hah!), or spend even more time or money getting/training a BLOPS alt?

1. Get into a fast, cloaky ship (CovOps cloak)
2. Learn how to travel in low/null
3. Read up on the different pirate factions you want to try out, get a feel for the type of opponents & weps they use. Train up your optimal defenses and weps
4. Get intimately familiar with DotLan or Ombey Maps; plan your route
5. Take your cloaky ship out there, scout around, and get to know the locals.

Joining a renter corp will probably help, but you need to be ready for a CTA. Joining a member corp means you will HAVE to be ready for a CTA. All the other silliness above means time, money, and isk. Plan first, take a cheap cloaky out there, and scout around. By getting to know some of the people out there may help you cut a lot of the non-sense short.

here's one out of left field:

Go to lowsec. I suggest Ardar area, it seems to be rife with wormholes. Live there for a week or so. Eventually a wormhole will spawn direct to nullsec. Take your BS through said wormhole, rat. Rat some more. If idiots come to shoot you, you warp back to the wormhole and jump to lowsec.

Alternately, get yourself into a C2 wormhole with a D382/A239 (C2 and lowsec) static pair. These tend to be rather quiet. Aside from access to lowsec ratting, C2 sites, and nubs to kill while they do their PI business, eventually the D382 will connect to a C2 with E545/N062 static pair.

Move in to this, as most will be empty. Refer wormhole forum for ideas, but generally, a small caldari POS with 2 months fuel (outlay, 160M) is all you need. You will then have unlimited opportunities to access nullsec of all varieties for anomalies, belt ratting, radars and mags (or whatever they are called these days).

Best is of course to join a corporation in one of these wormholes, but they tend to be asocial neckbeards, which on current perceptions gives you a good chance (birds of a feather and all that) but realistically, there aren't many of these people who recruit openly on the forums.

The advantage of wormhole access is, firstly, it is very low-risk. No bubbles, no massive 56 jump epic pilgrimages to Sanctum Mecca, no camps and camping-in station. Secondly, it is free; no jumps, no fuel, no lost covops.

Of course, it takes a lot of effort. But at least in my experience, it's one a week in the Essin constellation, and once there, you just live from a GSC loaded with missiles or ammo. Or better yet, use something with lasers and spnd nothing. Rat until you get jumped and podded, and ensure you make more than 500% of the replacement value of your ratting ship. Well worth it.

From what I've heard the easiest way to get to null is via HED-GP. Honest.

Lol, don't knock it. I recently waltzed right thru EC-P8R, and on to an extensive tour of Deklein, no camps no nothing. Now I wasn't doing PvE, and I do have a cov ops cloak so that might discourage hunters but those high-null gates are wide open sometimes.

To the OP, scout it out, learn how to live in null, join a corp or use the excelent WH idea given here.
If you want to solo it without the wormhole, scout first. Take a cov ops cloak ship up to your target area, scout around, make bookmarks: safes, perches and instaundocks. Take note of the natives. Try and figure out who the active PvP types are so that you can watchlist them. Who likes to lay gate camps and where. This will help greatly in living in null and hopefully help you plan your move.

Seconding this. My corp moved into Providence a few months ago. As long as you play nice with the locals, it's an easy way to try out the nullsec experience.

There are also numerous NPC stations where you may find battleships for sale. Also check contracts.

Just fly down there and buy one.