Career Mode 1.0 and later, how do you advance to Mun landing tech?

[Skovde]

It is pretty difficult to acquire science in order to reach all the different tech tiers required for the first flag planting on Mun... Anyone have any tips on which science tasks should be targeted for quicker advancement?

[ghpstage]

I managed a Minmus landing on my fourth launch on hard difficulty. The rocket I used could more than likely achieve a Mun landing instead, and if not I definately had more than was necessary to do it.

A large chunk of the science came from the scientists new ability to reset material bays and goo pods. It allows you to spam science experiments while keeping weight and costs vey low.
While in orbit on my second launch I upgraded the astro complex for EVA, spammed EVA reports and reused the mat bay and goo to grab experiments from 4 biomes, flying at Kerbin, high atmosphere, low space and high space. The mission got me 150 science points, with the material bay providing 60 by itself.

[Lei]

There are also several biomes in and around the space center, make those kerbals lose some weight and run them over, or make a plane or car with experiments onboard and drive them there! Free science!

Also contracts can be great for getting extra science. There is plenty around KSC to get you started!

[KhanIndustries]

In addition to the science you get from the different biomes at Kerbin (ocean, grassland, mountains, poles, KSC and every building located there) & missions etc.. I found launching probes is a great way to get an "advance" on the science you get from someplace that may be currently out of reach for a manned mission due to your tech.

Launching probes is pretty easy and cheap because you don't have to worry about lifiting off with the weight of pesky things like having enough fuel for a landing and getting back home. Just sending a QBE probe to the Mun with a temp, bara and science jr gets you a portion of the science (which is still worth quite a bit) for taking those readings on the way, while in orbit, landing and transmitting back home. The temp and bara can be done over and over for each area you travel through. You can pick up the remainder of the data's worth when you finally get there and do those same experiments again by hand when you get a Kerbin there.

Thats what I did anyway when I realized my tech (expecially my rocketry and fuel tech) was too far behind to do a Mun landing at the time. Best of luck.

[Bodkins(UK)]

Upgrade buildings so you can get soil samples. 120 points per sample and on minmus with its low gravity you can use monopropelant jets to scoot around various locations when you get it. You also wont need a ladder. The kerbals jetpack will cover that issue.

[MarQan]

What?
Everything you can.
Where?
Horizontal: near KSC buildings, Shore, Water, Grassland, Highlands and Desert biomes.
Vertical: Low-High Atmo and Low-High Space, Mun/Minmus fly by.

Material Study and Surface Samples have the highest science yield, but I assume you can't collect Surface Samples yet.
That leaves Science Jr, Mystery Goo, Thermometer, Crew- and EVA reports; in-flight EVA report requires an Astronaut Complex upgrade.

Most biomes are pretty straightforward, but:
Highlands: west from KSC.
Desert: west-south-western shores of the continent.
You can also get to the Ice Caps fairly easily, and if you flight straight towards north from KSC, you'll come across a Mountain biome halfway.

Depending on your skill/experience you might need to upgrade Tracking Station for Patched Conics and Mission Control for Flight Planning.
This should help to plan more efficient maneuvers, requiring less parts, or less advanced ones.

Having all the 45-science research and Heavy Rocketry should be enough for a Mun/Minmus fly by: the Kickback solid booster will help keeping your parts count low on manned missions.

Getting Electrics will allow you to transmit data and do multiple experiments.

There are obviously shorter and better ways to get to a Mun-landing, but this proved to be a solid strategy. I want to say foolproof, but nothing is foolproof in KSP.